Showing remarkable insight into the relationship between language and thought, Alan Turing in 1950 proposed the Imitation Game as a proxy for the question “Can machines think?” and its meaning and practicality have been debated hotly ever since. The Imitation Game has come under criticism within the Computer Science and Artificial Intelligence communities with leading scientists proposing alternatives, revisions, or even that the Game be abandoned entirely. Yet Turing’s imagined conversational fragments between human and machine are rich with complex instances (...) of inference of implied information, reasoning from generalizations, and meta-reasoning, challenges AI practitioners have wrestled with since at least 1980 and continue to study. We argue that the very fact the Imitation Game is so difficult may be the very reason it shouldn’t be changed or abandoned. The semi-decidability of the game at this point hints at the possibility of a hard limit to the powers of technology. (shrink)

Logic has been a—disputed—ingredient in the emergence and development of the now very large field known as knowledge representation and reasoning. In this book (in progress), I select some central topics in this highly fruitful, albeit controversial, association (e.g., non-monotonic reasoning, implicit belief, logical omniscience, closed world assumption), identifying their sources and analyzing/explaining their elaboration in highly influential published work.

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyze their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. LogicProgrammingisacomputationalparadigmthathasproducedcompu- tationallyattractivesystemswithremarkablesuccessinmanyapplications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation engine (...) to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use in applications. (shrink)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

This is a position paper concerning the role of empirical studies of human default reasoning in the formalization of AI theories of default reasoning. We note that AI motivates its theoretical enterprise by reference to human skill at default reasoning, but that the actual research does not make any use of this sort of information and instead relies on intuitions of individual investigators. We discuss two reasons theorists might not consider human performance relevant to formalizing default reasoning: (a) that intuitions (...) are sufficient to describe a model, and (b) that human performance in this arena is irrelevant to a competence model of the phenomenon. We provide arguments against both these reasons. We then bring forward three further considerations against the use of intuitions in this arena: (a) it leads to an unawareness of predicate ambiguity, (b) it presumes an understanding of ordinary language statements of typicality, and (c) it is similar to discredited views in other fields. We advocate empirical investigation of the range of human phenomena that intuitively embody default reasoning. Gathering such information would provide data with which to generate formal default theories and against which to test the claims of proposed theories. Our position is that such data are the very phenomena that default theories are supposed to explain. (shrink)

The basic theory of scientific understanding presented in Sections 1–2 exploits three main ideas.First, that to understand a phenomenonP (for a given agent) is to be able to fitP into the cognitive background corpusC (of the agent).Second, that to fitP intoC is to connectP with parts ofC (via arguments in a very broad sense) such that the unification ofC increases.Third, that the cognitive changes involved in unification can be treated as sequences of shifts of phenomena inC. How the theory fits (...) typical examples of understanding and how it excludes spurious unifications is explained in detail. Section 3 gives a formal description of the structure of cognitive corpuses which contain descriptive as well as inferential components. The theory of unification is then refined in the light of so called puzzling phenomena, to enable important distinctions, such as that between consonant and dissonant understanding. In Section 4, the refined theory is applied to several examples, among them a case study of the development of the atomic model. The final part contains a classification of kinds of understanding and a discussion of the relation between understanding and explanation. (shrink)

This paper is an attempt to bring together two separated areas of research: classical mathematics and metamathematics on the one side, non-monotonic reasoning on the other. This is done by simulating nonmonotonic logic through antitonic theory extensions. In the first half, the specific extension procedure proposed here is motivated informally, partly in comparison with some well-known non-monotonic formalisms. Operators V and, more generally, U are obtained which have some plausibility when viewed as giving nonmonotonic theory extensions. In the second half, (...) these operators are treated from a mathematical and metamathematical point of view. Here an important role is played by U -closed theories and U -fixed points. The last section contains results on V-closed theories which are specific for V. (shrink)

It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

Reasoning almost always occurs in the face of incomplete information. Such reasoning is nonmonotonic in the sense that conclusions drawn may later be withdrawn when additional information is obtained. There is an active literature on the problem of modeling such nonmonotonic reasoning, yet no category of method-let alone a single method-has been broadly accepted as the right approach. This paper introduces a new method, called sweeping presumptions, for modeling nonmonotonic reasoning. The main goal of the paper is to provide an (...) example-driven, nontechnical introduction to the method of sweeping presumptions, and thereby to make it plausible that sweeping presumptions can usefully be applied to the problems of nonmonotonic reasoning. The paper discusses a representative sample of examples that have appeared in the literature on nonmonotonic reasoning, and discusses them from the point of view of sweeping presumptions. (shrink)

When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics (...) for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours. (shrink)

Online collection of papers by Devitt, Dretske, Guarino, Hochberg, Jackson, Petitot, Searle, Tye, Varzi and other leading thinkers on philosophy and the foundations of cognitive Science. Topics dealt with include: Wittgenstein and Cognitive Science, Content and Object, Logic and Foundations, Language and Linguistics, and Ontology and Mereology.

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)

With recent advancements in systems engineering and artificial intelligence, autonomous agents are increasingly being called upon to execute tasks that have normative relevance. These are tasks that directly—and potentially adversely—affect human well-being and demand of the agent a degree of normative-sensitivity and -compliance. Such norms and normative principles are typically of a social, legal, ethical, empathetic, or cultural (‘SLEEC’) nature. Whereas norms of this type are often framed in the abstract, or as high-level principles, addressing normative concerns in concrete applications (...) of autonomous agents requires the refinement of normative principles into explicitly formulated practical rules. This paper develops a process for deriving specification rules from a set of high-level norms, thereby bridging the gap between normative principles and operational practice. This enables autonomous agents to select and execute the most normatively favourable action in the intended context premised on a range of underlying relevant normative principles. In the translation and reduction of normative principles to SLEEC rules, we present an iterative process that uncovers normative principles, addresses SLEEC concerns, identifies and resolves SLEEC conflicts, and generates both preliminary and complex normatively-relevant rules, thereby guiding the development of autonomous agents and better positioning them as normatively SLEEC-sensitive or SLEEC-compliant. (shrink)

The history of science can be better understood against the background of a history of knowledge comprising not only theoretical but also intuitive and practical knowledge. This widening of scope necessitates a more concise definition of the concept of knowledge, relating its cognitive to its material and social dimensions. The history of knowledge comprises the history of institutions in which knowledge is produced and transmitted. This is an essential but hitherto neglected aspect of cultural evolution. Taking this aspect into account (...) one is led to the concept of extended evolution, which integrates the perspectives of niche construction and complex regulative networks. The paper illustrates this concept using four examples: the emergence of language, the Neolithic revolution, the invention of writing and the origin of mechanics. (shrink)

Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...) present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance. (shrink)

The paper provides a preliminary study of algebraic semantics for modal and superintuitionistic non-monotonic logics. The main question answered is: how can non-monotonic inference be understood algebraically?

We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

There has been considerable discussion in the past about the assumptions and basis of different ethical rules. For instance, it is commonplace to say that ethical rules are defaults rules, which means that they tolerate exceptions. Some authors argue that morality can only be grounded in particular cases while others defend the existence of general principles related to ethical rules. Our purpose here is not to justify either position, but to try to model general ethical rules with artificial intelligence formalisms (...) and to compute logical consequences of different ethical theories. More precisely, this is an attempt to show that progress in non-monotonic logics, which simulates default reasoning, could provide a way to formalize different ethical conceptions. From a technical point of view, the model developed in this paper makes use of the Answer Set Programming (ASP) formalism. It is applied comparatively to different ethical systems with respect to their attitude towards lying. The advantages of such formalization are two-fold: firstly, to clarify ideas and assumptions, and, secondly, to use solvers to derive consequences of different ethical conceptions automatically, which can help in a rigorous comparison of ethical theories. (shrink)

The notion of the rational closure of a positive knowledge base K of conditional assertions θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} (standing for if θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} then normally φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}) was first introduced by Lehmann (1989) and developed by Lehmann and Magidor (...) (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice, however, one might expect a knowledge base to consist not just of positive conditional assertions, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}, but also negative conditional assertions, θi φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} (standing for not if θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} then normally φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}. Restricting ourselves to a finite language we show that the rational closure still exists for satisfiable knowledge bases containing both positive and negative conditional assertions and has similar properties to those exhibited in Lehmann and Magidor (1992). In particular an algorithm in Lehmann and Magidor (1992) which constructs the rational closure can be adapted to this case and yields, in turn, completeness theorems for the conditional assertions entailed by such a mixed knowledge base. (shrink)

Pickering and Chater (P&C) maintain that folk psychology and cognitive science should neither compete nor cooperate. Each is an independent enterprise, with a distinct subject matter and characteristic modes of explanation. P&C''s case depends upon their characterizations of cognitive science and folk psychology. We question the basis for their characterizations, challenge both the coherence and the individual adequacy of their contrasts between the two, and show that they waver in their views about the scope of each. We conclude that P&C (...) do not so muchdiscover ascreate the gap they find between folk psychology and cognitive science. It is an artifact of their implausible and unmotivated attempt to demarcate the two areas, and of the excessively narrow accounts they give of each. (shrink)

With recent advancements in systems engineering and artificial intelligence, autonomous agents are increasingly being called upon to execute tasks that have normative relevance. These are tasks that directly—and potentially adversely—affect human well-being and demand of the agent a degree of normative-sensitivity and -compliance. Such norms and normative principles are typically of a social, legal, ethical, empathetic, or cultural nature. Whereas norms of this type are often framed in the abstract, or as high-level principles, addressing normative concerns in concrete applications of (...) autonomous agents requires the refinement of normative principles into explicitly formulated practical rules. This paper develops a process for deriving specification rules from a set of high-level norms, thereby bridging the gap between normative principles and operational practice. This enables autonomous agents to select and execute the most normatively favourable action in the intended context premised on a range of underlying relevant normative principles. In the translation and reduction of normative principles to SLEEC rules, we present an iterative process that uncovers normative principles, addresses SLEEC concerns, identifies and resolves SLEEC conflicts, and generates both preliminary and complex normatively-relevant rules, thereby guiding the development of autonomous agents and better positioning them as normatively SLEEC-sensitive or SLEEC-compliant. (shrink)

This article presents results from a simulation‐based study of inheritance inference, that is, inference from the typicality of a property among a “base” class to its typicality among a subclass of the class. The study aims to ascertain which kinds of inheritance inferences are reliable, with attention to the dependence of their reliability upon the type of environment in which inferences are made. For example, the study addresses whether inheritance inference is reliable in the case of “exceptional subclasses” (i.e., subclasses (...) that are known to be atypical in some respect) and attends to variations in reliability that result from variations in the entropy level of the environment. A further goal of the study is to show that the reliability of inheritance inference depends crucially on which sorts of base classes are used in making inferences. One approach to inheritance inference treats the extension of any atomic predicate as a suitable base class. A second approach identifies suitable base classes with the cells of a partition (of a preselected size k) of the domain of objects that satisfies the condition of maximizing the similarity of objects that are assigned to the same class. In addition to permitting more inferences, our study shows that the second approach results in inheritance inferences that are far more reliable, particularly in the case of exceptional subclasses. (shrink)

The present paper analyses the topic of scientific discovery and the problem of the existence of a logical framework involved in such endeavour. We inquire how several non-monotonic logic frameworks and other formalisms can account for such a task. In the same vein, we analyse some key aspects of the historical and theoretical debate surrounding scientific discovery, in particular, the context of discovery and context of justification context distinction. We present an argument concerning the weakening of the discovery/justification context dichotomy (...) based on the descriptive accent contained in the non-monotonic logic perspective together with its epistemological concerns. (shrink)

We investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of Circumscription. First, we give a proof of the failure of the Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P; Z-minimal models of a first-order sentence is Δ-elementary, then it is elementary. That is, whenever the circumscription of a first-order sentence is equivalent to a first-order theory, then it is equivalent to a finitely axiomatizable one. This means that classes of (...) models of circumscribed theories are either elementary or not Δ-elementary. Finally, using the previous result, we prove that, whenever a relation Pi is defined in the class of P; Z-minimal models of a first-order sentence Φ and whenever such class of P; Z-minimal models is Δ-elementary, then there is an explicit definition ψ for Pi such that the class of P; Z-minimal models of Φ is the class of models of Φ ∧ ψ. In order words, the circumscription of P in Φ with Z varied can be replaced by Φ plus this explicit definition ψ for Pi. (shrink)

Much previous work in artificial intelligence has neglected representing time in all its complexity. In particular, it has neglected continuous change and the indeterminacy of the future. To rectify this, I have developed a first‐order temporal logic, in which it is possible to name and prove things about facts, events, plans, and world histories. In particular, the logic provides analyses of causality, continuous change in quantities, the persistence of facts (the frame problem), and the relationship between tasks and actions. It (...) may be possible to implement a temporal‐inference machine based on this logic, which keeps track of several “maps” of a time line, one per possible history. (shrink)