## New Ideas in Neuro Symbolic Reasoning and Learning SpringerLink

# Symbolic Reasoning Symbolic AI and Machine Learning Pathmind

As an illustration of errors that arise in reasoning with sentences in natural language, consider the following examples. In the first, we use the transitivity of the better relation to derive a conclusion about the relative quality of champagne and soda from the relative quality of champagne and beer and the relative quality or beer and soda. One of Aristotle’s great contributions to philosophy was the identification of syntactic operations that . By applying rules of inference to premises, we produce conclusions that are entailed by those premises.

LNNs are a modification of today’s neural networks so that they become equivalent to a set of logic statements — yet they also retain the original learning capability of a neural network. Standard neurons are modified so that they precisely model operations in With real-valued logic, variables can take on values in a continuous range between 0 and 1, rather than just binary values of ‘true’ or ‘false.’real-valued logic. LNNs are able to model formal logical reasoning by applying a recursive neural computation of truth values that moves both forward and backward (whereas a standard neural network only moves forward).

The course presumes that the student understands sets and set operations, such as union, intersection, and complement. The course also presumes that the student is comfortable with symbolic mathematics, at the level of high-school algebra. However, it has been used by motivated secondary school students and post-graduate professionals interested in honing their logical reasoning skills.

LISP provided the first read-eval-print loop to support rapid program development. Compiled functions could be freely mixed with interpreted functions. Program tracing, stepping, and breakpoints were also provided, along with the ability to change values or functions and continue from breakpoints or errors.

By 2015, his hostility toward all things symbols had fully crystallized. He gave a talk at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest mistakes. Alain Colmerauer and Philippe Roussel are credited as the inventors of Prolog. Prolog is a form of logic programming, which was invented by Robert Kowalski.

Many leading scientists believe that symbolic reasoning will continue to remain a very important component of artificial intelligence. But the benefits of deep learning and neural networks are not without tradeoffs. Deep learning has several deep challenges and disadvantages in comparison to symbolic AI. Notably, deep learning algorithms are opaque, and figuring out how they work perplexes even their creators. And it’s very hard to communicate and troubleshoot their inner-workings.

One of the most successful neural network architectures have been the Convolutional Neural Networks (CNNs) [3]⁴ (tracing back to 1982’s Neocognitron [5]). The distinguishing features introduced in CNNs were the use of shared weights and the idea of pooling. Cohen’s meticulous design process for Aaron included defining the proportions of the human hand and introducing the concept https://chat.openai.com/ of compositionality. His rule-based system enabled AARON to distinguish how to draw subjects in various spatial relationships, a challenge that modern AI systems still wrestle with. Say whether each of the following sentences is logically entailed by these sentences. In the hopes of preventing difficulties, it is worth pointing out a potential source of confusion.

Third, it is symbolic, with the capacity of performing causal deduction and generalization. Fourth, the symbols and the links between them are transparent to us, and thus we will know what it has learned or not – which is the key for the security of an AI system. Fifth, its transparency enables it to learn with relatively small data. Last but not least, it is more friendly to unsupervised learning than DNN. We present the details of the model, the algorithm powering its automatic learning ability, and describe its usefulness in different use cases. The purpose of this paper is to generate broad interest to develop it within an open source project centered on the Deep Symbolic Network (DSN) model towards the development of general AI.

## Title:Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions

It achieves a form of “symbolic disentanglement”, offering one solution to the important problem of disentangled representations and invariance. Basic computations of the network include predicting high-level objects and their properties from low-level objects and binding/aggregating relevant objects together. These computations operate at a more fundamental level than convolutions, capturing convolution as a special case while being significantly more general than it. All operations are executed in an input-driven fashion, thus sparsity and dynamic computation per sample are naturally supported, complementing recent popular ideas of dynamic networks and may enable new types of hardware accelerations. We experimentally show on CIFAR-10 that it can perform flexible visual processing, rivaling the performance of ConvNet, but without using any convolution.

- LNN performs necessary reasoning such as type-based and geographic reasoning to eventually return the answers for the given question.
- If we know the state of the world, then we should write enough sentences to communicate this to others.
- These similarities allow us to compare the logics and to gain an appreciation of the fundamental tradeoff between expressiveness and computational complexity.
- Although symbolic reasoning often conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures.

Logic is important in all of these disciplines, and it is essential in computer science. Yet it is rarely offered as a standalone course, making it more difficult for students to succeed and get better quality jobs. The ancient Greeks thought Logic sufficiently important that it was one of the three subjects in the Greek educational Trivium, along with what is symbolic reasoning Grammar and Rhetoric. Oddly, Logic occupies a relatively small place in the modern school curriculum. We have courses in the Sciences and various branches of Mathematics, but very few secondary schools offer courses in Logic; and it is not required in most university programs. Just because we use Logic does not mean we are necessarily good at it.

## Extant Accounts of Symbolic Reasoning

A key component of the system architecture for all expert systems is the knowledge base, which stores facts and rules for problem-solving.[53]

The simplest approach for an expert system knowledge base is simply a collection or network of production rules. Production rules connect symbols in a relationship similar to an If-Then statement. The expert system processes the rules to make deductions and to determine what additional information it needs, i.e. what questions to ask, using human-readable symbols.

Logic may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true. We do not need to know anything about the concepts in our premises except for the information expressed in those premises. Furthermore, while our conclusion must be true if our premises are true, it can be false if one or more of our premises is false. Effective communication requires a language that allows us to express what we know, no more and no less. If we know the state of the world, then we should write enough sentences to communicate this to others.

Insofar as mathematical rule-following emerges from active engagement with physical notations, the mathematical rule-follower is a distributed system that spans the boundaries between brain, body, and environment. For this interlocking to promote mathematically appropriate behavior, however, the relevant perceptual and sensorimotor mechanisms must be just as well-trained as the physical notations must be well-designed. Thus, on one hand, the development of symbolic reasoning abilities in an individual subject will depend on the development of a sophisticated sensorimotor skillset in the way outlined above. A corollary of the claim that symbolic and other forms of mathematical and logical reasoning are grounded in a wide variety of sensorimotor skills is that symbolic reasoning is likely to be both idiosyncratic and context-specific. For one, different individuals may rely on different embodied strategies, depending on their particular history of experience and engagement with particular notational systems.

## Toward a Constitutive Account: The Cyborg View

Using a formal language eliminates such unintentional ambiguities (and, for better or worse, avoids any unintentional humor as well). So far, we have illustrated everything with sentences in English. While natural language works well in many circumstances, it is not without its problems. Natural language sentences can be complex; they can be ambiguous; and failing to understand the meaning of a sentence can lead to errors in reasoning.

In academic program sheets, we might have constraints on how many courses of varying types that students must take. Data Integration The language of Logic can be used to relate the vocabulary and structure of disparate data sources, and automated reasoning techniques can be used to integrate the data in these sources. Engineers can use the language of Logic to write specifications for their products and to encode their designs.

As ‘common sense’ AI matures, it will be possible to use it for better customer support, business intelligence, medical informatics, advanced discovery, and much more. Similarly, Allen’s temporal interval algebra is a simplification of reasoning about time and Region Connection Calculus is a simplification of reasoning about spatial relationships. Cognitive architectures such as ACT-R may have additional capabilities, such as the ability to compile frequently used knowledge into higher-level chunks. A more flexible kind of problem-solving occurs when reasoning about what to do next occurs, rather than simply choosing one of the available actions. This kind of meta-level reasoning is used in Soar and in the BB1 blackboard architecture.

By augmenting and combining the strengths of statistical AI, like machine learning, with the capabilities of human-like symbolic knowledge and reasoning, we’re aiming to create a revolution in AI, rather than an evolution. Harold Cohen’s work with AARON provides an interesting historical parallel. Over 50 years ago, Cohen used a symbolic rule-based system to help Aaron understand how to draw elements like the human hand and spatial relationships.

What can we conclude from the bits of information in our sample logical sentences? Since there are different values in different worlds, we cannot say yes and we cannot say no. However, we do not have enough information to say which case is correct.

## From Philosophy to Thinking Machines

It contains sentences about sentences; it contains proofs about proofs. In some places, we use similar mathematical symbology both for sentences in Logic and sentences about Logic. Wherever possible, we try to be clear about this distinction, but the potential for confusion remains. These similarities allow us to compare the logics and to gain an appreciation of the fundamental tradeoff between expressiveness and computational complexity.

The fourth sentence says that one condition holds or another but does not say which. The fifth sentence gives a general fact about the girls Abby likes. Using OOP, you can create extensive and complex symbolic AI programs that perform various tasks. Many of the concepts and tools you find in computer science are the results of these efforts. Symbolic AI programs are based on creating explicit structures and behavior rules.

## How AI will transform planning, scheduling, and risk management in the…

Having already perfected a mechanical calculator for arithmetic, he argued that, with this universal algebra, it would be possible to build a machine capable of rendering the consequences of such a system mechanically. We can use this operation to solve the problem of Mary’s love life. Looking at the two premises above, we notice that p occurs on the left-hand side of one sentence and the right-hand side of the other. Consequently, we can cancel the p and thereby derive the conclusion that, if is Monday and raining, then Mary loves Quincy or Mary loves Quincy. As with Algebra, Formal Logic defines certain operations that we can use to manipulate expressions.

Carl and his postdocs were world-class experts in mass spectrometry. We began to add to their knowledge, inventing knowledge of engineering as we went along. These experiments amounted to titrating DENDRAL more and more knowledge.

The translational view easily accounts for cases in which individual symbols are more readily perceived based on external format. Perceptual Manipulations Theory also predicts this sort of impact, but further predicts that perceived structures will affect the application of rules—since rules are presumed to be implemented via systems involved in perceiving that structure. In this section, we will review several empirical sources of evidence for the impact of visual structure on the implementation of formal rules.

- First of all, every deep neural net trained by supervised learning combines deep learning and symbolic manipulation, at least in a rudimentary sense.
- In particular, in each case, there is a language with a formal syntax and a precise semantics; there is a notion of logical entailment; and there are legal rules for manipulating expressions in the language.
- Perceptual Manipulations Theory suggests that most symbolic reasoning emerges from the ways in which notational formalisms are perceived and manipulated.

The potential for a satisfying unification of the successes and failures of human symbolic and other forms of mathematical reasoning under a common set of mechanisms provides us with the confidence to claim that this is a topic worthy of further investigation, both empirical and philosophical. Perceptual Manipulations Theory suggests that most symbolic reasoning emerges from the ways in which notational formalisms are perceived and manipulated. Nevertheless, direct sensorimotor processing of physical stimuli is augmented by the capacity to imagine and manipulate mental representations of notational markings. Insofar as our account emphasizes perceptual representations of formal notations and imagined notation-manipulations, it can be contrasted with Barsalou’s perceptual symbol systems account, in which “people often construct non-formal simulations to solve formal problems” (Barsalou, 1999, 606). Moreover, our emphasis differs from standard “conceptual metaphor” accounts, which suggest that formal reasoners rely on a “semantic backdrop” of embodied experiences and sensorimotor capacities to interpret abstract mathematical concepts. Our account is probably closest to one articulated by Dörfler (2002), who like us emphasizes the importance of treating elements of notational systems as physical objects rather than as meaning-carrying symbols.

The grandfather of AI, Thomas Hobbes said — Thinking is manipulation of symbols and Reasoning is computation. P.J.B. performed the research, contributed new analytical tools and analyzed data. McCarthy’s approach to fix the frame problem was circumscription, a kind of non-monotonic logic where deductions could be made from actions that need only specify what would change while not having to explicitly specify everything that would not change. Other non-monotonic logics provided truth maintenance systems that revised beliefs leading to contradictions.

## 5 Symbolic Logic

Incomplete induction is the basis for Science (and machine learning). We can try solving algebraic equations by randomly trying different values for the variables in those equations. However, we can usually get to an answer faster by manipulating our equations syntactically. Rather than checking all worlds, we simply apply syntactic operations to the premises we are given to generate conclusions. Unfortunately, in general, there are many, many possible worlds; and, in some cases, the number of possible worlds is infinite, in which case model checking is impossible. Given two sentences, we know the world must be in the intersection of the set of worlds in which the first sentence is true and the set of worlds in which the second sentence is true.

Nevertheless, there is probably no uniquely correct answer to the question of how people do mathematics. Indeed, it is important to consider the relative merits of all competing accounts and to incorporate the best elements of each. Although we believe that most of our mathematical abilities are rooted in our past experience and engagement with notations, we do not depend on these notations at all times.

Unlike deep learning, which relies on patterns and statistical methods, symbolic AI uses explicit representations of problems, logic, and rules to derive conclusions. This approach allows for more interpretability and precision in specific tasks, making it ideal for applications requiring clear reasoning and decision-making processes. The synergy between continuous information processing that characterizes deep learning and large language models and discrete information extraction and reasoning of symbolic AI is what we call neurosymbolic AI. The Symbolic AI paradigm led to seminal ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and reasoning systems.

Symbolic artificial intelligence, also known as Good, Old-Fashioned AI (GOFAI), was the dominant paradigm in the AI community from the post-War era until the late 1980s. We hope that by now you’re convinced that symbolic AI is a must when it comes to NLP applied to chatbots. Machine learning can be applied to lots of disciplines, and one of those is Natural Language Processing, which is used in AI-powered conversational chatbots. We note that this was the state at the time and the situation has changed quite considerably in the recent years, with a number of modern NSI approaches dealing with the problem quite properly now. However, to be fair, such is the case with any standard learning model, such as SVMs or tree ensembles, which are essentially propositional, too.

By contrast, several of the sentences are false in the world on the right. The universe is written in the language of mathematics and its characters are triangles, circles, and other geometric objects. René Descartes, a mathematician, and philosopher, regarded thoughts themselves as symbolic representations and Perception as an internal process. Not as the repeated application of formal Euclidean axioms, but as “magic motion,” in which a term moves to the other side of the equation and “flips” sign. Landy and Goldstone (2009) suggest that this reference to motion is no mere metaphor. Subjects with significant training in calculus found it easier to solve problems of this form when an irrelevant field of background dots moved in the same direction as the variables, than when the dots moved in the contrary direction.

Such formal representations and methods are useful for us to use ourselves. Moreover, they allow us to automate the process of deduction, though the computability of such implementations varies with the complexity of the sentences involved. Perceptual Manipulations Theory (PMT) goes further than the cyborg account in emphasizing the perceptual nature of symbolic reasoning.

Symbolic AI (or Classical AI) is the branch of artificial intelligence research that concerns itself with attempting to explicitly represent human knowledge in a declarative form (i.e. facts and rules). If such an approach is to be successful in producing human-like intelligence then it is necessary to translate often implicit or procedural knowledge possessed by humans into an explicit form using symbols and rules for their manipulation. Artificial systems mimicking human expertise such as Expert Systems are emerging in a variety of fields that constitute narrow but deep knowledge domains. Like interlocking puzzle pieces that together form a larger image, sensorimotor mechanisms and physical notations “interlock” to produce sophisticated mathematical behaviors.

Satplan is an approach to planning where a planning problem is reduced to a Boolean satisfiability problem. Marvin Minsky first proposed frames as a way of interpreting common visual situations, such as an office, and Roger Schank extended this idea to scripts for common routines, such as dining out. Cyc has attempted to capture useful common-sense knowledge and has “micro-theories” to handle particular kinds of domain-specific reasoning. Forward chaining inference engines are the most common, and are seen in CLIPS and OPS5. Backward chaining occurs in Prolog, where a more limited logical representation is used, Horn Clauses. Programs were themselves data structures that other programs could operate on, allowing the easy definition of higher-level languages.

Typically, the first step in solving such a problem is to express the information in the form of equations. If we let x represent the age of Xavier and y represent the age of Yolanda, we can capture the essential information of the problem as shown below. Now, it is noteworthy that there are patterns of reasoning that are not always correct but are sometimes useful. One solution is to take pictures of your cat from different angles and create new rules for your application to compare each input against all those images.

They can also be used to describe other symbols (a cat with fluffy ears, a red carpet, etc.). We hope this work also inspires a next generation of thinking and capabilities in AI. The next step for us is to tackle successively more difficult question-answering tasks, for example those that test complex temporal reasoning and handling of incompleteness Chat GPT and inconsistencies in knowledge bases. There are several flavors of question answering (QA) tasks – text-based QA, context-based QA (in the context of interaction or dialog) or knowledge-based QA (KBQA). We chose to focus on KBQA because such tasks truly demand advanced reasoning such as multi-hop, quantitative, geographic, and temporal reasoning.

If we do not know which of various ways the world could be, we need a language that allows us to express only what we know, i.e. which worlds are possible and which are not. The language of Logic gives us a means to express incomplete information when that is all we have and to express complete information when full information is available. Logical sentences like the ones above constrain the possible ways the world could be.

We then see some of the problems with the use of natural language and see how those problems can be mitigated through the use of Symbolic Logic. Finally, we discuss the automation of logical reasoning and some of the computer applications that this makes possible. Question-answering is the first major use case for the LNN technology we’ve developed. While achieving state-of-the-art performance on the two KBQA datasets is an advance over other AI approaches, these datasets do not display the full range of complexities that our neuro-symbolic approach can address. In particular, the level of reasoning required by these questions is relatively simple. LNNs’ form of real-valued logic also enables representation of the strengths of relationships between logical clauses via neural weights, further improving its predictive accuracy.3 Another advantage of LNNs is that they are tolerant to incomplete knowledge.

1) Hinton, Yann LeCun and Andrew Ng have all suggested that work on unsupervised learning (learning from unlabeled data) will lead to our next breakthroughs. Deep learning has its discontents, and many of them look to other branches of AI when they hope for the future. It’s a jack-of-all-trades, finding its way into computer science to steer algorithms and into mathematics to underpin proofs.

We introduce the Deep Symbolic Network (DSN) model, which aims at becoming the white-box version of Deep Neural Networks (DNN). The DSN model provides a simple, universal yet powerful structure, similar to DNN, to represent any knowledge of the world, which is transparent to humans. The conjecture behind the DSN model is that any type of real world objects sharing enough common features are mapped into human brains as a symbol. Those symbols are connected by links, representing the composition, correlation, causality, or other relationships between them, forming a deep, hierarchical symbolic network structure.

The paper argues that language is primarily a tool for communication rather than a mechanism for thought and reasoning. This perspective highlights the development course for AI systems, particularly concerning the recent research on large language models (LLMs). There are also some topics that are relevant to Logic but are out of scope for this course, such as probability, metaknowledge (knowledge about knowledge), and paradoxes (e.g. This sentence is false.). Also, negation as failure (knowing not versus not knowing, non-deductive reasoning methods (like induction), and paraconsistent reasoning (i.e. reasoning from inconsistent premises). We touch on these extensions in this course, but we do not talk about them in any depth.

But in recent years, as neural networks, also known as connectionist AI, gained traction, symbolic AI has fallen by the wayside. Although we will emphasize the kinds of algebra, arithmetic, and logic that are typically learned in high school, our view also potentially explains the activities of advanced mathematicians—especially those that involve representational structures like graphs and diagrams. Our major goal, therefore, is to provide a novel and unified account of both successful and unsuccessful episodes of symbolic reasoning, with an eye toward providing an account of mathematical reasoning in general. Before turning to our own account, however, we begin with a brief outline of some more traditional views. A second flaw in symbolic reasoning is that the computer itself doesn’t know what the symbols mean; i.e. they are not necessarily linked to any other representations of the world in a non-symbolic way. Again, this stands in contrast to neural nets, which can link symbols to vectorized representations of the data, which are in turn just translations of raw sensory data.

On our view, the way in which physical notations are perceived is at least as important as the way in which they are actively manipulated. Building on the foundations of deep learning and symbolic AI, we have developed technology that can answer complex questions with minimal domain-specific training. Initial results are very encouraging – the system outperforms current state-of-the-art techniques on two prominent datasets with no need for specialized end-to-end training. The two biggest flaws of deep learning are its lack of model interpretability (i.e. why did my model make that prediction?) and the large amount of data that deep neural networks require in order to learn. The two biggest flaws of deep learning are its lack of model interpretability (i.e. why did my model make that prediction?) and the amount of data that deep neural networks require in order to learn. However, as imagined by Bengio, such a direct neural-symbolic correspondence was insurmountably limited to the aforementioned propositional logic setting.

Symbolic artificial intelligence showed early progress at the dawn of AI and computing. You can easily visualize the logic of rule-based programs, communicate them, and troubleshoot them. In this work, we approach KBQA with the basic premise that if we can correctly translate the natural language questions into an abstract form that captures the question’s conceptual meaning, we can reason over existing knowledge to answer complex questions. Table 1 illustrates the kinds of questions NSQA can handle and the form of reasoning required to answer different questions. This approach provides interpretability, generalizability, and robustness— all critical requirements in enterprise NLP settings .

However, if we see enough cases in which something is true and we never see a case in which it is false, we tend to conclude that it is always true. Unfortunately, when induction is incomplete, as in this case, it is not sound. If we replace x by Toyotas and y by cars and z by made in America, we get the following line of argument, leading to a conclusion that happens to be correct. You can foun additiona information about ai customer service and artificial intelligence and NLP. As an example of a rule of inference, consider the reasoning step shown below.

We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures. Other ways of handling more open-ended domains included probabilistic reasoning systems and machine learning to learn new concepts and rules.

For example, there are four different worlds that satisfy the sentences in the previous section. Maybe in the future, we’ll invent AI technologies that can both reason and learn. But for the moment, symbolic AI is the leading method to deal with problems that require logical thinking and knowledge representation. Hobbes was influenced by Galileo, just as Galileo thought that geometry could represent motion, Furthermore, as per Descartes, geometry can be expressed as algebra, which is the study of mathematical symbols and the rules for manipulating these symbols.

No explicit series of actions is required, as is the case with imperative programming languages. The key AI programming 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.

It dissects our statements, revealing their structure in stark clarity. It’s as vital as a compass for a sailor, guiding us through a sea of potentially confusing dialogues. When we’re debating life’s big questions or when we want to be sure we’re on solid ground with our reasoning, symbolic logic shines as a beacon of clarity. Don’t get us wrong, machine learning is an amazing tool that enables us to unlock great potential and AI disciplines such as image recognition or voice recognition, but when it comes to NLP, we’re firmly convinced that machine learning is not the best technology to be used.

That is, a symbol offers a level of abstraction above the concrete and granular details of our sensory experience, an abstraction that allows us to transfer what we’ve learned in one place to a problem we may encounter somewhere else. In a certain sense, every abstract category, like chair, asserts an analogy between all the disparate objects called chairs, and we transfer our knowledge about one chair to another with the help of the symbol. Insofar as computers suffered from the same chokepoints, their builders relied on all-too-human hacks like symbols to sidestep the limits to processing, storage and I/O. As computational capacities grow, the way we digitize and process our analog reality can also expand, until we are juggling billion-parameter tensors instead of seven-character strings. If machine learning can appear as a revolutionary approach at first, its lack of transparency and a large amount of data that is required in order for the system to learn are its two main flaws. Companies now realize how important it is to have a transparent AI, not only for ethical reasons but also for operational ones, and the deterministic (or symbolic) approach is now becoming popular again.