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Symbolic Artificial Intelligence
In expert system, symbolic expert system (likewise called classical artificial intelligence or logic-based expert system) [1] [2] is the term for the collection of all techniques in artificial intelligence research study that are based upon top-level symbolic (human-readable) representations of problems, logic and search. [3] Symbolic AI utilized tools such as reasoning programming, production guidelines, semantic webs and frames, and it established applications such as knowledge-based systems (in specific, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm resulted in influential ideas in search, symbolic programming languages, representatives, multi-agent systems, the semantic web, and the strengths and limitations of official knowledge and thinking systems.
Symbolic AI was the dominant paradigm of AI research from the mid-1950s till the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic approaches would ultimately be successful in creating a maker with artificial basic intelligence and considered this the supreme goal of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to unrealistic expectations and guarantees and was followed by the first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) accompanied the rise of specialist systems, their pledge of recording corporate know-how, and a passionate corporate accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later frustration. [8] Problems with troubles in knowledge acquisition, keeping large knowledge bases, and brittleness in managing out-of-domain problems developed. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists focused on addressing hidden issues in dealing with uncertainty and in knowledge acquisition. [10] Uncertainty was attended to with formal approaches such as concealed Markov designs, Bayesian reasoning, and statistical relational learning. [11] [12] Symbolic maker finding out addressed the knowledge acquisition problem with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive logic shows to find out relations. [13]
Neural networks, a subsymbolic approach, had actually been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron knowing work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not considered as effective until about 2012: ”Until Big Data ended up being prevalent, the general agreement in the Al community was that the so-called neural-network approach was helpless. Systems simply didn’t work that well, compared to other approaches. … A transformation came in 2012, when a variety of individuals, including a team of scientists working with Hinton, exercised a method to use the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next several years, deep knowing had magnificent success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and maker translation. However, since 2020, as inherent difficulties with bias, explanation, comprehensibility, and robustness became more obvious with deep knowing approaches; an increasing variety of AI scientists have called for combining the finest of both the symbolic and neural network techniques [17] [18] and addressing areas that both techniques have trouble with, such as common-sense thinking. [16]
A short history of symbolic AI to today day follows listed below. Time periods and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia article on the History of AI, with dates and titles differing a little for increased clarity.
The very first AI summertime: irrational enthusiasm, 1948-1966
Success at early attempts in AI occurred in 3 primary areas: artificial neural networks, knowledge representation, and heuristic search, contributing to high expectations. This section sums up Kautz’s reprise of early AI history.
Approaches motivated by human or animal cognition or habits
Cybernetic methods tried to replicate the feedback loops in between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and seven vacuum tubes for control, based on a preprogrammed neural internet, was developed as early as 1948. This work can be seen as an early precursor to later work in neural networks, reinforcement knowing, and located robotics. [20]
An essential early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to prove 38 primary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to develop a domain-independent issue solver, GPS (General Problem Solver). GPS fixed issues represented with formal operators via state-space search using means-ends analysis. [21]
During the 1960s, symbolic techniques accomplished terrific success at replicating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was focused in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own design of research. Earlier approaches based on cybernetics or artificial neural networks were deserted or pressed into the background.
Herbert Simon and Allen Newell studied human problem-solving abilities and tried to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as cognitive science, operations research study and management science. Their research study team used the outcomes of mental experiments to develop programs that simulated the techniques that individuals used to solve problems. [22] [23] This tradition, focused at Carnegie Mellon University would eventually culminate in the advancement of the Soar architecture in the middle 1980s. [24] [25]
Heuristic search
In addition to the highly specialized domain-specific kinds of understanding that we will see later used in expert systems, early symbolic AI researchers discovered another more general application of understanding. These were called heuristics, general rules that assist a search in promising directions: ”How can non-enumerative search be useful when the underlying issue is greatly tough? The approach advocated by Simon and Newell is to utilize heuristics: fast algorithms that might stop working on some inputs or output suboptimal services.” [26] Another crucial advance was to find a method to use these heuristics that ensures a solution will be discovered, if there is one, not holding up against the occasional fallibility of heuristics: ”The A * algorithm offered a general frame for complete and optimum heuristically directed search. A * is used as a subroutine within practically every AI algorithm today but is still no magic bullet; its assurance of efficiency is bought at the cost of worst-case rapid time. [26]
Early deal with understanding representation and reasoning
Early work covered both applications of formal reasoning emphasizing first-order reasoning, together with attempts to deal with sensible reasoning in a less formal manner.
Modeling official thinking with reasoning: the ”neats”
Unlike Simon and Newell, John McCarthy felt that devices did not need to simulate the specific mechanisms of human idea, however could instead attempt to find the essence of abstract reasoning and analytical with logic, [27] despite whether individuals used the exact same algorithms. [a] His lab at Stanford (SAIL) focused on utilizing official logic to fix a variety of issues, consisting of knowledge representation, preparation and learning. [31] Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which resulted in the advancement of the programming language Prolog and the science of logic programming. [32] [33]
Modeling implicit sensible knowledge with frames and scripts: the ”scruffies”
Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that resolving hard issues in vision and natural language processing required advertisement hoc solutions-they argued that no easy and basic concept (like logic) would capture all the elements of intelligent behavior. Roger Schank described their ”anti-logic” techniques as ”shabby” (instead of the ”cool” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of ”scruffy” AI, given that they must be constructed by hand, one complex principle at a time. [38] [39] [40]
The first AI winter: crushed dreams, 1967-1977
The very first AI winter season was a shock:
During the very first AI summer, many individuals believed that device intelligence could be attained in simply a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research study to use AI to fix issues of nationwide security; in particular, to automate the translation of Russian to English for intelligence operations and to create self-governing tanks for the battleground. Researchers had actually begun to recognize that achieving AI was going to be much harder than was expected a years previously, however a mix of hubris and disingenuousness led numerous university and think-tank researchers to accept financing with guarantees of deliverables that they must have understood they could not meet. By the mid-1960s neither useful natural language translation systems nor autonomous tanks had been created, and a significant backlash embeded in. New DARPA leadership canceled existing AI funding programs.
Outside of the United States, the most fertile ground for AI research was the UK. The AI winter in the United Kingdom was stimulated on not so much by dissatisfied military leaders as by rival academics who viewed AI researchers as charlatans and a drain on research study funding. A teacher of applied mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research study in the country. The report specified that all of the problems being worked on in AI would be much better handled by researchers from other disciplines-such as applied mathematics. The report likewise claimed that AI successes on toy problems might never ever scale to real-world applications due to combinatorial surge. [41]
The 2nd AI summertime: understanding is power, 1978-1987
Knowledge-based systems
As restrictions with weak, domain-independent approaches became increasingly more apparent, [42] researchers from all 3 customs started to construct understanding into AI applications. [43] [7] The understanding transformation was driven by the realization that understanding underlies high-performance, domain-specific AI applications.
Edward Feigenbaum said:
– ”In the knowledge lies the power.” [44]
to explain that high performance in a specific domain needs both basic and extremely domain-specific knowledge. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:
( 1) The Knowledge Principle: if a program is to carry out an intricate job well, it needs to know a lot about the world in which it operates.
( 2) A plausible extension of that principle, called the Breadth Hypothesis: there are 2 additional capabilities needed for intelligent habits in unforeseen situations: drawing on increasingly general knowledge, and analogizing to specific however remote understanding. [45]
Success with expert systems
This ”understanding transformation” caused the advancement and implementation of professional systems (introduced by Edward Feigenbaum), the very first commercially successful kind of AI software application. [46] [47] [48]
Key specialist systems were:
DENDRAL, which discovered the structure of natural molecules from their chemical formula and mass spectrometer readings.
MYCIN, which identified bacteremia – and suggested more laboratory tests, when essential – by translating lab outcomes, client history, and medical professional observations. ”With about 450 rules, MYCIN had the ability to carry out in addition to some professionals, and significantly better than junior medical professionals.” [49] INTERNIST and CADUCEUS which took on internal medication medical diagnosis. Internist attempted to catch the proficiency of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could ultimately detect approximately 1000 different illness.
– GUIDON, which showed how an understanding base constructed for expert issue solving could be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then tiresome process that could take up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is thought about the very first expert system that count on knowledge-intensive analytical. It is explained below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:
One of individuals at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I told him I wanted an induction ”sandbox”, he stated, ”I have just the one for you.” His lab was doing mass spectrometry of amino acids. The question was: how do you go from taking a look at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we began the DENDRAL Project: I was excellent at heuristic search approaches, and he had an algorithm that was good at generating the chemical problem area.
We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, inventor of the chemical behind the birth control pill, and also among the world’s most appreciated mass spectrometrists. Carl and his postdocs were first-rate specialists in mass spectrometry. We started to contribute to their knowledge, creating understanding of engineering as we went along. These experiments amounted to titrating DENDRAL a growing number of understanding. The more you did that, the smarter the program ended up being. We had excellent outcomes.
The generalization was: in the knowledge lies the power. That was the huge concept. In my profession that is the substantial, ”Ah ha!,” and it wasn’t the way AI was being done previously. Sounds basic, however it’s most likely AI’s most effective generalization. [51]
The other professional systems pointed out above came after DENDRAL. MYCIN exemplifies the classic expert system architecture of a knowledge-base of rules combined to a symbolic reasoning mechanism, consisting of making use of certainty aspects to handle unpredictability. GUIDON reveals how an explicit knowledge base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a specific type of knowledge-based application. Clancey showed that it was not adequate simply to use MYCIN’s guidelines for direction, but that he likewise needed to include rules for discussion management and student modeling. [50] XCON is significant since of the millions of dollars it conserved DEC, which set off the professional system boom where most all major corporations in the US had professional systems groups, to capture corporate knowledge, protect it, and automate it:
By 1988, DEC’s AI group had 40 specialist systems deployed, with more en route. DuPont had 100 in use and 500 in advancement. Nearly every significant U.S. corporation had its own Al group and was either utilizing or examining professional systems. [49]
Chess professional understanding was encoded in Deep Blue. In 1996, this permitted IBM’s Deep Blue, with the aid of symbolic AI, to win in a game of chess versus the world champion at that time, Garry Kasparov. [52]
Architecture of knowledge-based and skilled systems
An essential element of the system architecture for all professional systems is the knowledge base, which stores truths and rules for analytical. [53] The simplest technique for a skilled system understanding base is merely a collection or network of production guidelines. Production rules link symbols in a relationship comparable to an If-Then statement. The professional system processes the rules to make deductions and to identify what extra info it needs, i.e. what concerns to ask, utilizing human-readable symbols. For instance, OPS5, CLIPS and their successors Jess and Drools operate in this fashion.
Expert systems can run in either a forward chaining – from evidence to conclusions – or backwards chaining – from goals to required information and prerequisites – way. Advanced knowledge-based systems, such as Soar can also carry out meta-level thinking, that is thinking about their own thinking in regards to deciding how to resolve issues and keeping track of the success of problem-solving methods.
Blackboard systems are a 2nd type of knowledge-based or professional system architecture. They model a community of specialists incrementally contributing, where they can, to resolve a problem. The problem is represented in numerous levels of abstraction or alternate views. The specialists (knowledge sources) volunteer their services whenever they recognize they can contribute. Potential analytical actions are represented on a program that is upgraded as the issue situation changes. A controller decides how helpful each contribution is, and who ought to make the next analytical action. One example, the BB1 chalkboard architecture [54] was originally influenced by studies of how humans prepare to perform numerous tasks in a trip. [55] An innovation of BB1 was to use the very same chalkboard model to resolving its control issue, i.e., its controller performed meta-level reasoning with understanding sources that kept track of how well a plan or the problem-solving was continuing and could change from one technique to another as conditions – such as goals or times – altered. BB1 has actually been used in numerous domains: building and construction site preparation, smart tutoring systems, and real-time patient monitoring.
The 2nd AI winter season, 1988-1993
At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were offering LISP makers particularly targeted to accelerate the advancement of AI applications and research study. In addition, several expert system companies, such as Teknowledge and Inference Corporation, were offering skilled system shells, training, and seeking advice from to corporations.
Unfortunately, the AI boom did not last and Kautz finest explains the second AI winter season that followed:
Many reasons can be used for the arrival of the second AI winter season. The hardware business failed when far more cost-effective basic Unix workstations from Sun together with good compilers for LISP and Prolog came onto the market. Many commercial implementations of professional systems were discontinued when they proved too pricey to preserve. Medical expert systems never captured on for a number of reasons: the problem in keeping them up to date; the obstacle for physician to find out how to use a bewildering range of different expert systems for different medical conditions; and possibly most crucially, the reluctance of doctors to rely on a computer-made diagnosis over their gut instinct, even for specific domains where the professional systems might outperform a typical medical professional. Equity capital money deserted AI almost overnight. The world AI conference IJCAI hosted an enormous and luxurious exhibition and thousands of nonacademic participants in 1987 in Vancouver; the main AI conference the following year, AAAI 1988 in St. Paul, was a little and strictly scholastic affair. [9]
Including more extensive foundations, 1993-2011
Uncertain thinking
Both statistical methods and extensions to reasoning were tried.
One statistical technique, concealed Markov models, had already been promoted in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized making use of Bayesian Networks as a sound however efficient way of dealing with uncertain thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian approaches were applied effectively in professional systems. [57] Even later, in the 1990s, analytical relational learning, a technique that integrates likelihood with sensible solutions, allowed probability to be combined with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.
Other, non-probabilistic extensions to first-order reasoning to assistance were likewise tried. For instance, non-monotonic thinking might be used with reality upkeep systems. A truth upkeep system tracked assumptions and validations for all inferences. It enabled reasonings to be withdrawn when assumptions were discovered out to be inaccurate or a contradiction was derived. Explanations might be offered a reasoning by discussing which guidelines were used to produce it and then continuing through underlying inferences and guidelines all the method back to root assumptions. [58] Lofti Zadeh had actually introduced a various kind of extension to manage the representation of ambiguity. For example, in choosing how ”heavy” or ”tall” a man is, there is regularly no clear ”yes” or ”no” response, and a predicate for heavy or tall would instead return worths in between 0 and 1. Those values represented to what degree the predicates were real. His fuzzy logic even more provided a way for propagating combinations of these values through sensible solutions. [59]
Artificial intelligence
Symbolic machine discovering techniques were examined to deal with the understanding acquisition traffic jam. One of the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test technique to produce plausible rule hypotheses to test versus spectra. Domain and task knowledge reduced the variety of prospects tested to a manageable size. Feigenbaum described Meta-DENDRAL as
… the conclusion of my imagine the early to mid-1960s pertaining to theory formation. The conception was that you had a problem solver like DENDRAL that took some inputs and produced an output. In doing so, it utilized layers of understanding to guide and prune the search. That knowledge acted because we spoke with individuals. But how did the individuals get the understanding? By taking a look at countless spectra. So we desired a program that would look at thousands of spectra and presume the knowledge of mass spectrometry that DENDRAL might utilize to solve private hypothesis formation issues. We did it. We were even able to release new understanding of mass spectrometry in the Journal of the American Chemical Society, providing credit just in a footnote that a program, Meta-DENDRAL, really did it. We had the ability to do something that had been a dream: to have a computer system program created a new and publishable piece of science. [51]
In contrast to the knowledge-intensive technique of Meta-DENDRAL, Ross Quinlan created a domain-independent approach to statistical category, choice tree knowing, beginning initially with ID3 [60] and after that later on extending its capabilities to C4.5. [61] The choice trees created are glass box, interpretable classifiers, with human-interpretable category guidelines.
Advances were made in comprehending artificial intelligence theory, too. Tom Mitchell introduced version space learning which explains learning as an explore an area of hypotheses, with upper, more basic, and lower, more specific, borders encompassing all viable hypotheses constant with the examples seen up until now. [62] More officially, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of maker knowing. [63]
Symbolic device learning encompassed more than discovering by example. E.g., John Anderson provided a cognitive model of human learning where ability practice results in a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a student may find out to apply ”Supplementary angles are 2 angles whose measures sum 180 degrees” as numerous different procedural rules. E.g., one rule might state that if X and Y are supplemental and you understand X, then Y will be 180 – X. He called his technique ”knowledge compilation”. ACT-R has been utilized successfully to design elements of human cognition, such as learning and retention. ACT-R is likewise utilized in smart tutoring systems, called cognitive tutors, to successfully teach geometry, computer shows, and algebra to school children. [64]
Inductive logic programs was another approach to finding out that allowed logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could manufacture Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to create hereditary programs, which he utilized to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic technique to program synthesis that manufactures a practical program in the course of showing its specs to be appropriate. [66]
As an alternative to reasoning, Roger Schank presented case-based thinking (CBR). The CBR method described in his book, Dynamic Memory, [67] focuses first on keeping in mind essential analytical cases for future usage and generalizing them where suitable. When confronted with a new issue, CBR retrieves the most comparable previous case and adapts it to the specifics of the current issue. [68] Another alternative to reasoning, genetic algorithms and genetic programs are based upon an evolutionary model of learning, where sets of rules are encoded into populations, the guidelines govern the habits of individuals, and selection of the fittest prunes out sets of inappropriate guidelines over lots of generations. [69]
Symbolic artificial intelligence was used to finding out principles, guidelines, heuristics, and analytical. Approaches, aside from those above, include:
1. Learning from guideline or advice-i.e., taking human guideline, impersonated advice, and identifying how to operationalize it in particular scenarios. For example, in a video game of Hearts, finding out exactly how to play a hand to ”prevent taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter professional (SME) feedback during training. When analytical fails, querying the professional to either discover a brand-new exemplar for analytical or to discover a brand-new explanation regarding precisely why one exemplar is more appropriate than another. For example, the program Protos learned to detect ringing in the ears cases by engaging with an audiologist. [71] 3. Learning by analogy-constructing problem solutions based on similar issues seen in the past, and then customizing their services to fit a brand-new circumstance or domain. [72] [73] 4. Apprentice knowing systems-learning novel options to issues by observing human analytical. Domain understanding describes why novel services are proper and how the option can be generalized. LEAP found out how to design VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing jobs to perform experiments and then learning from the outcomes. Doug Lenat’s Eurisko, for example, discovered heuristics to beat human gamers at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for useful macro-operators to be gained from series of fundamental analytical actions. Good macro-operators streamline problem-solving by allowing issues to be solved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now
With the rise of deep learning, the symbolic AI approach has been compared to deep learning as complementary ”… with parallels having actually been drawn lot of times by AI researchers between Kahneman’s research study on human reasoning and decision making – reflected in his book Thinking, Fast and Slow – and the so-called ”AI systems 1 and 2″, which would in principle be designed by deep learning and symbolic reasoning, respectively.” In this view, symbolic thinking is more apt for deliberative reasoning, preparation, and description while deep knowing is more apt for quick pattern recognition in perceptual applications with loud data. [17] [18]
Neuro-symbolic AI: incorporating neural and symbolic approaches
Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a manner that addresses strengths and weaknesses of each, in a complementary fashion, in order to support robust AI capable of reasoning, finding out, and cognitive modeling. As argued by Valiant [77] and lots of others, [78] the reliable construction of rich computational cognitive designs demands the mix of sound symbolic reasoning and efficient (maker) knowing designs. Gary Marcus, likewise, argues that: ”We can not construct rich cognitive models in an adequate, automatic way without the triumvirate of hybrid architecture, rich anticipation, and sophisticated methods for thinking.”, [79] and in particular: ”To develop a robust, knowledge-driven approach to AI we need to have the equipment of symbol-manipulation in our toolkit. Too much of beneficial understanding is abstract to make do without tools that represent and manipulate abstraction, and to date, the only machinery that we understand of that can control such abstract understanding reliably is the apparatus of sign manipulation. ” [80]
Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a requirement to address the 2 kinds of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two parts, System 1 and System 2. System 1 is quick, automated, user-friendly and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind utilized for pattern acknowledgment while System 2 is far much better suited for preparation, reduction, and deliberative thinking. In this view, deep knowing finest designs the first sort of thinking while symbolic thinking finest designs the 2nd kind and both are needed.
Garcez and Lamb explain research study in this area as being continuous for a minimum of the previous twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic thinking has been held every year because 2005, see http://www.neural-symbolic.org/ for information.
In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:
The integration of the symbolic and connectionist paradigms of AI has been pursued by a reasonably little research study neighborhood over the last 2 decades and has yielded a number of considerable outcomes. Over the last decade, neural symbolic systems have been shown efficient in overcoming the so-called propositional fixation of neural networks, as McCarthy (1988) put it in response to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were shown capable of representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and pieces of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been applied to a variety of problems in the areas of bioinformatics, control engineering, software application verification and adjustment, visual intelligence, ontology learning, and video game. [78]
Approaches for combination are differed. Henry Kautz’s taxonomy of neuro-symbolic architectures, together with some examples, follows:
– Symbolic Neural symbolic-is the existing method of numerous neural designs in natural language processing, where words or subword tokens are both the supreme input and output of big language models. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic strategies are utilized to call neural methods. In this case the symbolic approach is Monte Carlo tree search and the neural methods discover how to assess game positions.
– Neural|Symbolic-uses a neural architecture to analyze affective information as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to produce or label training data that is consequently found out by a deep knowing model, e.g., to train a neural model for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to develop or identify examples.
– Neural _ Symbolic -utilizes a neural net that is generated from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree created from understanding base rules and terms. Logic Tensor Networks [86] also fall under this classification.
– Neural [Symbolic] -allows a neural model to straight call a symbolic reasoning engine, e.g., to carry out an action or assess a state.
Many key research study questions remain, such as:
– What is the very best method to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should sensible understanding be learned and reasoned about?
– How can abstract understanding that is difficult to encode logically be managed?
Techniques and contributions
This section supplies an overview of strategies and contributions in a general context causing many other, more detailed short articles in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered earlier in the history section.
AI programming languages
The crucial AI programs language in the US during the last symbolic AI boom period was LISP. LISP is the second oldest programming language after FORTRAN and was created in 1958 by John McCarthy. LISP supplied the very first read-eval-print loop to support rapid program advancement. Compiled functions might be easily mixed with translated functions. Program tracing, stepping, and breakpoints were likewise supplied, together with the capability to alter values or functions and continue from breakpoints or mistakes. It had the first self-hosting compiler, implying that the compiler itself was initially written in LISP and after that ran interpretively to compile the compiler code.
Other essential developments originated by LISP that have actually infected other programs languages include:
Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals
Programs were themselves data structures that other programs might operate on, enabling the simple definition of higher-level languages.
In contrast to the US, in Europe the key AI programs language during that same period was Prolog. Prolog supplied a built-in shop of facts and provisions that could be queried by a read-eval-print loop. The shop could act as a knowledge base and the clauses could function as rules or a limited form of logic. As a subset of first-order logic Prolog was based upon Horn provisions with a closed-world assumption-any realities not understood were thought about false-and a distinct name presumption for primitive terms-e.g., the identifier barack_obama was considered to describe exactly one things. Backtracking and unification are built-in to Prolog.
Alain Colmerauer and Philippe Roussel are credited as the innovators of Prolog. Prolog is a type of logic programs, which was invented by Robert Kowalski. Its history was also influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of approaches. For more information see the area on the origins of Prolog in the PLANNER short article.
Prolog is also a type of declarative programs. The reasoning provisions that describe programs are directly translated to run the programs specified. No specific series of actions is required, as holds true with necessary programming languages.
Japan championed Prolog for its Fifth Generation Project, meaning to build special hardware for high efficiency. Similarly, LISP devices were built to run LISP, however as the 2nd AI boom turned to bust these companies might not compete with brand-new workstations that could now run LISP or Prolog natively at similar speeds. See the history area for more information.
Smalltalk was another prominent AI shows language. For instance, it introduced metaclasses and, in addition to Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current basic Lisp dialect. CLOS is a Lisp-based object-oriented system that enables numerous inheritance, in addition to incremental extensions to both classes and metaclasses, therefore providing a run-time meta-object protocol. [88]
For other AI programs languages see this list of programs languages for artificial intelligence. Currently, Python, a multi-paradigm programs language, is the most popular programming language, partly due to its comprehensive bundle library that supports data science, natural language processing, and deep learning. Python consists of a read-eval-print loop, functional elements such as higher-order functions, and object-oriented programming that consists of metaclasses.
Search
Search occurs in many type of problem fixing, consisting of preparation, restriction fulfillment, and playing games such as checkers, chess, and go. The very best understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven clause knowing, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.
Knowledge representation and reasoning
Multiple different methods to represent understanding and then reason with those representations have actually been examined. Below is a quick overview of methods to knowledge representation and automated thinking.
Knowledge representation
Semantic networks, conceptual charts, frames, and logic are all methods to modeling knowledge such as domain understanding, analytical understanding, and the semantic significance of language. Ontologies design crucial concepts and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be utilized for any domain while WordNet is a lexical resource that can also be considered as an ontology. YAGO includes WordNet as part of its ontology, to align facts drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being used.
Description logic is a reasoning for automated classification of ontologies and for detecting irregular category data. OWL is a language utilized to represent ontologies with description logic. Protégé is an ontology editor that can read in OWL ontologies and then examine consistency with deductive classifiers such as such as HermiT. [89]
First-order logic is more basic than description reasoning. The automated theorem provers gone over listed below can show theorems in first-order logic. Horn stipulation logic is more limited than first-order logic and is utilized in logic programs languages such as Prolog. Extensions to first-order logic consist of temporal reasoning, to handle time; epistemic reasoning, to reason about agent understanding; modal logic, to deal with possibility and need; and probabilistic reasonings to handle logic and likelihood together.
Automatic theorem proving
Examples of automated theorem provers for first-order logic are:
Prover9.
ACL2.
Vampire.
Prover9 can be used in combination with the Mace4 model checker. ACL2 is a theorem prover that can deal with proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also referred to as Nqthm.
Reasoning in knowledge-based systems
Knowledge-based systems have an explicit knowledge base, generally of guidelines, to enhance reusability throughout domains by separating procedural code and domain knowledge. A separate inference engine procedures rules and adds, deletes, or modifies a knowledge store.
Forward chaining inference engines are the most typical, and are seen in CLIPS and OPS5. Backward chaining occurs in Prolog, where a more minimal logical representation is used, Horn Clauses. Pattern-matching, specifically marriage, is used in Prolog.
A more flexible type of analytical happens when thinking about what to do next happens, rather than just selecting one of the offered actions. This kind of meta-level reasoning is used in Soar and in the BB1 chalkboard architecture.
Cognitive architectures such as ACT-R may have additional capabilities, such as the ability to compile regularly used knowledge into higher-level chunks.
Commonsense reasoning
Marvin Minsky initially proposed frames as a method of analyzing typical visual circumstances, such as a workplace, and Roger Schank extended this concept to scripts for common regimens, such as dining out. Cyc has attempted to capture useful common-sense knowledge and has ”micro-theories” to handle particular sort of domain-specific reasoning.
Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human reasoning about ignorant physics, such as what takes place when we heat a liquid in a pot on the stove. We anticipate it to heat and perhaps boil over, although we might not understand its temperature, its boiling point, or other information, such as air pressure.
Similarly, Allen’s temporal period algebra is a simplification of thinking about time and Region Connection Calculus is a simplification of reasoning about spatial relationships. Both can be fixed with restriction solvers.
Constraints and constraint-based thinking
Constraint solvers carry out a more minimal sort of reasoning than first-order logic. They can streamline sets of spatiotemporal constraints, such as those for RCC or Temporal Algebra, in addition to fixing other kinds of puzzle issues, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic shows can be used to fix scheduling problems, for example with restraint dealing with guidelines (CHR).
Automated planning
The General Problem Solver (GPS) cast preparation as problem-solving utilized means-ends analysis to produce strategies. STRIPS took a different method, seeing planning as theorem proving. Graphplan takes a least-commitment method to planning, instead of sequentially selecting actions from an initial state, working forwards, or a goal state if working in reverse. Satplan is a method to planning where a preparation issue is decreased to a Boolean satisfiability issue.
Natural language processing
Natural language processing focuses on dealing with language as information to carry out jobs such as identifying subjects without necessarily comprehending the desired significance. Natural language understanding, on the other hand, constructs a significance representation and uses that for further processing, such as addressing concerns.
Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long managed by symbolic AI, however because improved by deep learning techniques. In symbolic AI, discourse representation theory and first-order reasoning have been used to represent sentence meanings. Latent semantic analysis (LSA) and specific semantic analysis likewise supplied vector representations of files. In the latter case, vector components are interpretable as principles called by Wikipedia short articles.
New deep learning methods based on Transformer models have now eclipsed these earlier symbolic AI methods and obtained advanced efficiency in natural language processing. However, Transformer models are nontransparent and do not yet produce human-interpretable semantic representations for sentences and files. Instead, they produce task-specific vectors where the significance of the vector elements is nontransparent.
Agents and multi-agent systems
Agents are autonomous systems embedded in an environment they view and act on in some sense. Russell and Norvig’s basic textbook on expert system is arranged to reflect agent architectures of increasing sophistication. [91] The elegance of agents differs from simple reactive representatives, to those with a model of the world and automated preparation abilities, potentially a BDI representative, i.e., one with beliefs, desires, and objectives – or additionally a reinforcement discovering model found out over time to select actions – up to a combination of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep knowing for understanding. [92]
In contrast, a multi-agent system consists of numerous representatives that interact among themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The agents require not all have the very same internal architecture. Advantages of multi-agent systems consist of the capability to divide work among the agents and to increase fault tolerance when agents are lost. Research issues consist of how representatives reach agreement, dispersed issue fixing, multi-agent learning, multi-agent preparation, and dispersed restriction optimization.
Controversies emerged from early on in symbolic AI, both within the field-e.g., between logicists (the pro-logic ”neats”) and non-logicists (the anti-logic ”scruffies”)- and in between those who accepted AI however turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mainly from philosophers, on intellectual grounds, however also from funding agencies, especially during the two AI winters.
The Frame Problem: knowledge representation obstacles for first-order reasoning
Limitations were found in using basic first-order reasoning to reason about dynamic domains. Problems were discovered both with concerns to specifying the prerequisites for an action to succeed and in providing axioms for what did not alter after an action was performed.
McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, ”Some Philosophical Problems from the Standpoint of .” [93] A basic example takes place in ”showing that a person person could enter conversation with another”, as an axiom asserting ”if a person has a telephone he still has it after looking up a number in the telephone book” would be needed for the deduction to succeed. Similar axioms would be required for other domain actions to define what did not alter.
A comparable problem, called the Qualification Problem, occurs in attempting to mention the prerequisites for an action to succeed. An unlimited number of pathological conditions can be pictured, e.g., a banana in a tailpipe could avoid a cars and truck from operating correctly.
McCarthy’s approach to fix the frame problem was circumscription, a sort of non-monotonic reasoning where reductions might be made from actions that require just specify what would change while not needing to explicitly specify whatever that would not change. Other non-monotonic logics supplied truth upkeep systems that revised beliefs resulting in contradictions.
Other ways of handling more open-ended domains consisted of probabilistic thinking systems and artificial intelligence to find out new principles and rules. McCarthy’s Advice Taker can be deemed an inspiration here, as it might integrate brand-new knowledge provided by a human in the type of assertions or guidelines. For example, experimental symbolic device finding out systems explored the ability to take top-level natural language recommendations and to analyze it into domain-specific actionable rules.
Similar to the issues in managing vibrant domains, sensible reasoning is likewise hard to record in official reasoning. Examples of sensible thinking consist of implicit thinking about how individuals think or basic knowledge of day-to-day events, things, and living creatures. This type of knowledge is considered granted and not deemed noteworthy. Common-sense reasoning is an open area of research and challenging both for symbolic systems (e.g., Cyc has tried to catch essential parts of this knowledge over more than a decade) and neural systems (e.g., self-driving cars and trucks that do not understand not to drive into cones or not to hit pedestrians strolling a bike).
McCarthy saw his Advice Taker as having common-sense, however his definition of common-sense was various than the one above. [94] He defined a program as having common sense ”if it immediately deduces for itself a sufficiently wide class of instant effects of anything it is informed and what it already understands. ”
Connectionist AI: philosophical obstacles and sociological conflicts
Connectionist approaches include earlier deal with neural networks, [95] such as perceptrons; work in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s advanced approaches, such as Transformers, GANs, and other operate in deep knowing.
Three philosophical positions [96] have actually been described amongst connectionists:
1. Implementationism-where connectionist architectures carry out the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is turned down absolutely, and connectionist architectures underlie intelligence and are completely sufficient to explain it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are considered as complementary and both are needed for intelligence
Olazaran, in his sociological history of the debates within the neural network neighborhood, described the moderate connectionism view as basically suitable with existing research in neuro-symbolic hybrids:
The 3rd and last position I want to analyze here is what I call the moderate connectionist view, a more eclectic view of the present argument in between connectionism and symbolic AI. Among the scientists who has elaborated this position most explicitly is Andy Clark, a theorist from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark defended hybrid (partially symbolic, partially connectionist) systems. He declared that (a minimum of) 2 type of theories are required in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern acknowledgment) connectionism has advantages over symbolic models. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative symbol manipulation processes) the symbolic paradigm uses appropriate designs, and not only ”approximations” (contrary to what extreme connectionists would claim). [97]
Gary Marcus has actually claimed that the animus in the deep learning neighborhood against symbolic techniques now might be more sociological than philosophical:
To believe that we can merely desert symbol-manipulation is to suspend shock.
And yet, for the a lot of part, that’s how most existing AI proceeds. Hinton and numerous others have actually attempted difficult to eradicate signs completely. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historic grudge-is that smart habits will emerge simply from the confluence of massive information and deep learning. Where classical computers and software application fix tasks by defining sets of symbol-manipulating rules committed to specific tasks, such as modifying a line in a word processor or carrying out a computation in a spreadsheet, neural networks generally attempt to resolve tasks by statistical approximation and gaining from examples.
According to Marcus, Geoffrey Hinton and his associates have been emphatically ”anti-symbolic”:
When deep knowing reemerged in 2012, it was with a type of take-no-prisoners attitude that has characterized many of the last years. By 2015, his hostility towards all things symbols had completely taken shape. He lectured at an AI workshop at Stanford comparing signs to aether, one of science’s biggest mistakes.
…
Since then, his anti-symbolic project has actually just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep learning in one of science’s essential journals, Nature. It closed with a direct attack on symbol manipulation, calling not for reconciliation but for outright replacement. Later, Hinton informed a gathering of European Union leaders that investing any further cash in symbol-manipulating approaches was ”a big mistake,” comparing it to investing in internal combustion engines in the age of electrical cars and trucks. [98]
Part of these disputes might be due to unclear terms:
Turing award winner Judea Pearl provides a review of device knowing which, regrettably, conflates the terms device learning and deep knowing. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of professional systems dispossessed of any capability to discover. Making use of the terms requires clarification. Artificial intelligence is not confined to association guideline mining, c.f. the body of work on symbolic ML and relational learning (the distinctions to deep learning being the choice of representation, localist sensible instead of dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not almost production rules written by hand. A correct meaning of AI concerns understanding representation and thinking, autonomous multi-agent systems, planning and argumentation, as well as learning. [99]
Situated robotics: the world as a model
Another review of symbolic AI is the embodied cognition approach:
The embodied cognition approach declares that it makes no sense to think about the brain separately: cognition happens within a body, which is embedded in an environment. We require to study the system as a whole; the brain’s operating exploits consistencies in its environment, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensing units become main, not peripheral. [100]
Rodney Brooks invented behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this method, is deemed an alternative to both symbolic AI and connectionist AI. His method rejected representations, either symbolic or distributed, as not only unnecessary, but as destructive. Instead, he developed the subsumption architecture, a layered architecture for embodied representatives. Each layer achieves a various purpose and needs to work in the real life. For instance, the very first robotic he explains in Intelligence Without Representation, has 3 layers. The bottom layer translates sonar sensing units to avoid things. The middle layer triggers the robot to roam around when there are no obstacles. The top layer causes the robotic to go to more far-off places for additional expedition. Each layer can momentarily inhibit or suppress a lower-level layer. He slammed AI scientists for defining AI issues for their systems, when: ”There is no tidy division in between understanding (abstraction) and reasoning in the genuine world.” [101] He called his robots ”Creatures” and each layer was ”composed of a fixed-topology network of basic limited state makers.” [102] In the Nouvelle AI method, ”First, it is essential to check the Creatures we build in the real life; i.e., in the very same world that we humans live in. It is dreadful to fall into the temptation of testing them in a streamlined world initially, even with the very best intentions of later moving activity to an unsimplified world.” [103] His emphasis on real-world testing was in contrast to ”Early operate in AI focused on games, geometrical problems, symbolic algebra, theorem proving, and other official systems” [104] and using the blocks world in symbolic AI systems such as SHRDLU.
Current views
Each approach-symbolic, connectionist, and behavior-based-has benefits, but has actually been criticized by the other techniques. Symbolic AI has actually been slammed as disembodied, liable to the certification issue, and bad in managing the perceptual problems where deep discovering excels. In turn, connectionist AI has actually been criticized as badly fit for deliberative detailed issue solving, integrating knowledge, and managing planning. Finally, Nouvelle AI stands out in reactive and real-world robotics domains however has actually been criticized for problems in including knowing and understanding.
Hybrid AIs integrating one or more of these approaches are currently deemed the course forward. [19] [81] [82] Russell and Norvig conclude that:
Overall, Dreyfus saw locations where AI did not have complete answers and stated that Al is for that reason difficult; we now see a number of these very same locations going through ongoing research study and advancement causing increased ability, not impossibility. [100]
Artificial intelligence.
Automated planning and scheduling
Automated theorem proving
Belief revision
Case-based reasoning
Cognitive architecture
Cognitive science
Connectionism
Constraint shows
Deep learning
First-order reasoning
GOFAI
History of expert system
Inductive logic shows
Knowledge-based systems
Knowledge representation and reasoning
Logic programs
Artificial intelligence
Model monitoring
Model-based thinking
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical symbol systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational knowing
Symbolic mathematics
YAGO ontology
WordNet
Notes
^ McCarthy when said: ”This is AI, so we don’t care if it’s psychologically genuine”. [4] McCarthy restated his position in 2006 at the AI@50 conference where he stated ”Expert system is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck composes that there are ”2 significant branches of artificial intelligence: one focused on producing smart behavior regardless of how it was achieved, and the other intended at modeling smart procedures found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote ”Aeronautical engineering texts do not define the goal of their field as making ’devices that fly so precisely like pigeons that they can fool even other pigeons.'” [30] Citations
^ Garnelo, Marta; Shanahan, Murray (October 2019). ”Reconciling deep learning with symbolic synthetic intelligence: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). ”Logic-Based Expert System”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). ”Reconciling deep learning with symbolic synthetic intelligence: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). ”Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). ”Backpropagation Applied to Handwritten Zip Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. ”Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. ”AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). ”An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
^ Lenat, Douglas B; Feigenbaum, Edward A (1988 ). ”On the thresholds of understanding”. Proceedings of the International Workshop on Expert System for Industrial Applications: 291-300. doi:10.1109/ AIIA.1988.13308. S2CID 11778085.
^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). ”An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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^ Spiegelhalter et al. 1993.
^ Russell & Norvig 2021, pp. 335-337.
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^ Shapiro, Ehud Y (1981 ). ”The Model Inference System”. Proceedings of the 7th worldwide joint conference on Artificial intelligence. IJCAI. Vol. 2. p. 1064.
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^ Bareiss, Ray; Porter, Bruce; Wier, Craig. ”Chapter 4: Protos: An Exemplar-Based Learning Apprentice”. In Michalski, Carbonell & Mitchell (1986 ), pp. 112-139.
^ Carbonell, Jaime. ”Chapter 5: Learning by Analogy: Formulating and Generalizing Plans from Past Experience”. In Michalski, Carbonell & Mitchell (1983 ), pp. 137-162.
^ Carbonell, Jaime. ”Chapter 14: Derivational Analogy: A Theory of Reconstructive Problem Solving and Expertise Acquisition”. In Michalski, Carbonell & Mitchell (1986 ), pp. 371-392.
^ Mitchell, Tom; Mabadevan, Sridbar; Steinberg, Louis. ”Chapter 10: LEAP: A Knowing Apprentice for VLSI Design”. In Kodratoff & Michalski (1990 ), pp. 271-289.
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^ Valiant 2008.
^ a b Garcez et al. 2015.
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^ Marcus 2020, p. 17.
^ a b Rossi 2022.
^ a b Selman 2022.
^ Garcez & Lamb 2020, p. 2.
^ Garcez et al. 2002.
^ Rocktäschel, Tim; Riedel, Sebastian (2016 ). ”Learning Knowledge Base Inference with Neural Theorem Provers”. Proceedings of the 5th Workshop on Automated Knowledge Base Construction. San Diego, CA: Association for Computational Linguistics. pp. 45-50. doi:10.18653/ v1/W16 -1309. Retrieved 2022-08-06.
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