ABSTRACT What characterizes human reasoning is the ability of dealing with incomplete information. Incomplete logic is developed for modeling incomplete knowledge. The most distinctive feature of incomplete logic is its semantics. This is an alternative presentation of partial semantics. In this paper, we will introduce the general notion of incomplete logic (ICL), compare it with partial logic, and give the resolution method for it. We will also show how ICL can be applied to nonmonotonic reasoning. We define nonmonotonic derivation as (...) monotonic derivation in ICL from the database and some consistent assumptions. The mechanism of ICL makes it easy to assert the consistency of an assumption without asserting the assumption itself. (shrink)

While the epistemic significance of disagreement has been a popular topic in epistemology for at least a decade, little attention has been paid to logical disagreement. This monograph is meant as a remedy. The text starts with an extensive literature review of the epistemology of (peer) disagreement and sets the stage for an epistemological study of logical disagreement. The guiding thread for the rest of the work is then three distinct readings of the ambiguous term ‘logical disagreement’. Chapters 1 and (...) 2 focus on the Ad Hoc Reading according to which logical disagreements occur when two subjects take incompatible doxastic attitudes toward a specific proposition in or about logic. Chapter 2 presents a new counterexample to the widely discussed Uniqueness Thesis. Chapters 3 and 4 focus on the Theory Choice Reading of ‘logical disagreement’. According to this interpretation, logical disagreements occur at the level of entire logical theories rather than individual entailment-claims. Chapter 4 concerns a key question from the philosophy of logic, viz., how we have epistemic justification for claims about logical consequence. In Chapters 5 and 6 we turn to the Akrasia Reading. On this reading, logical disagreements occur when there is a mismatch between the deductive strength of one’s background logic and the logical theory one prefers (officially). Chapter 6 introduces logical akrasia by analogy to epistemic akrasia and presents a novel dilemma. Chapter 7 revisits the epistemology of peer disagreement and argues that the epistemic significance of central principles from the literature are at best deflated in the context of logical disagreement. The chapter also develops a simple formal model of deep disagreement in Default Logic, relating this to our general discussion of logical disagreement. The monograph ends in an epilogue with some reflections on the potential epistemic significance of convergence in logical theorizing. (shrink)

In this book an introduction to the grammatical view of the scalar implicature phenomenon is presented. A detailed overview is offered concerning the embeddability of the exhaustivity operator, and the contextual dependance of the alternatives generation process. The theoretical implications of the grammatical view with respect to the abductive character of the scalar implicature are also discussed. A pragmatic account of the assertive content is proposed in correlation with a blindness-based account of the semantic content carried by scalar sentences, in (...) order to ensure that the information globally conveyed by the latter is sometimes different from the semantic content automatically generated. -/- . (shrink)

Summary. The viability of the proposal that human cognition involves the utilization of nonsentential models is seriously undercut by the fact that no one has yet given a satisfactory account of how neurophysiological circuitry might realize representations of the right sort. Such an account is offered up here, the general idea behind which is that high-level models can be realized by lower—level computations and, in turn, by neural machinations. It is shown that this account can be usefully applied to deal (...) with problems in fields ranging from artificial intelligence to the philosophy of science. (shrink)

Laws of nature take center stage in philosophy of science. Laws are usually believed to stand in a tight conceptual relation to many important key concepts such as causation, explanation, confirmation, determinism, counterfactuals etc. Traditionally, philosophers of science have focused on physical laws, which were taken to be at least true, universal statements that support counterfactual claims. But, although this claim about laws might be true with respect to physics, laws in the special sciences (such as biology, psychology, economics etc.) (...) appear to have—maybe not surprisingly—different features than the laws of physics. Special science laws—for instance, the economic law “Under the condition of perfect competition, an increase of demand of a commodity leads to an increase of price, given that the quantity of the supplied commodity remains constant” and, in biology, Mendel's Laws—are usually taken to “have exceptions”, to be “non-universal” or “to be ceteris paribus laws”. How and whether the laws of physics and the laws of the special sciences differ is one of the crucial questions motivating the debate on ceteris paribus laws. Another major, controversial question concerns the determination of the precise meaning of “ceteris paribus”. Philosophers have attempted to explicate the meaning of ceteris paribus clauses in different ways. The question of meaning is connected to the problem of empirical content, i.e., the question whether ceteris paribus laws have non-trivial and empirically testable content. Since many philosophers have argued that ceteris paribus laws lack empirically testable content, this problem constitutes a major challenge to a theory of ceteris paribus laws. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In these systems, (...) two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

Much of the philosophical discussion of explanations has centered around two broad conceptions of what sorts of ‘things’ explanations are – namely, the descriptive and ontic conceptions. Defenders of each argue that scientific psychology has at best little to contribute to the study of explanations. These anti-psychologistic arguments come in two main varieties, the metaphysical and the epistemic. Both varieties trace back to Hempel and recur in the more recent writings of prominent mechanists. The metaphysical arguments attempt to combat psychologism (...) about explanation by doubly dissociating explanations themselves from the commonly associated phenomenology of explanation. The epistemic arguments attempt to combat psychologism by doubly dissociating the good-making features of explanations from the CAPE. I focus on the metaphysical arguments here, for only they directly concern the nature of, as opposed to the evaluation conditions for, explanations. The metaphysical arguments are all shown to equivocate over ‘explanation’, and thus they are no threat to the proposal that sometimes explanations just are psychological events. Such arguments do, nonetheless, gesture towards something important – namely, that the CAPE is neither necessary nor sufficient for explanation in any sense. Similar considerations lead another latter-day mechanist to conclude that no phenomenology of any sort is essential for explanation. What all of these thinkers overlook, however, is that there is another important phenomenological correlate of explanation – namely, finding a happening intelligible or understanding how or why-possibly – and it may well be of the very essence of explanation, at least in the psychological sense. I propose a psychomechanistic theory of intelligibility that accounts for how we can, through finite means, make boundless, endlessly qualified inferences about the implications of our explanations. In closing I note that, although finding a happening intelligible does sometimes engender an unjustified confidence in correctness, we should not overlook how attaining this state does at least put us in a kind of epistemic base camp. I also hint at how intelligibility could turn out to be the ultimate source of the descriptive and ontic conceptions of explanation. (shrink)

Ordinary Language Philosophy has largely fallen out of favour, and with it the belief in the primary importance of analyses of ordinary language for philosophical purposes. Still, in their various endeavours, philosophers not only from analytic but also from other backgrounds refer to the use and meaning of terms of interest in ordinary parlance. In doing so, they most commonly appeal to their own linguistic intuitions. Often, the appeal to individual intuitions is supplemented by reference to dictionaries. In recent times, (...) Internet search engine queries for expressions of interest have become quite popular. Apparently, philosophers attempt to surpass the limits of their own linguistic intuitions by appealing to experts or to factual uses of language. I argue that this attempt is commendable but that its execution is wanting. Instead of appealing to dictionaries or Internet queries, philosophers should employ computer-based linguistic corpora in order to confirm or falsify hypotheses about the factual use of language. This approach also has some advantages over methods employed by experimental philosophers. If the importance of ordinary language is stressed, the use of linguistic corpora is hardly avoidable. (shrink)

A plan is made to fly from Glasgow to Moscow and is shown by circumscription to lead to the traveller arriving in Moscow. Then a fact about an unexpected obstacle---the traveller losing his ticket---is added without changing any of the previous facts, and the original plan can no longer be shown to work if it must take into account the new fact. However, an altered plan that includes buying a replacement ticket can now be shown to work. The formalism used (...) is a modification of one developed by Vladimir Lifschitz, and I have been informed that the modification isn't correct, and I should go back to Lifschitz's original formalism. April 14,2001: I still haven't done it, so this article has to be regarded as tentative. I hope to fix the problems without going back to Lifschitz's formalism, which I find awkward.}. (shrink)

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. A (...) proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (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)

Default reasoning occurs when the available information does not deductively guarantee the truth of the conclusion; and the conclusion is nonetheless correctly arrived at. The formalisms that have been developed in Artificial Intelligence to capture this mode of reasoning have suffered from a lack of agreement as to which non-monotonic inferences should be considered correct; and so Lifschitz 1989 produced a set of “Nonmonotonic Benchmark Problems” which all future formalisms are supposed to honor. The present work investigates the extent to (...) which humans follow the prescriptions set out in these Benchmark Problems. (shrink)

Review of a compendium of alternative formal representations of common-sense knowledge. The book is centered largely on formal representations drawn from first-order logic, and thus lies in the tradition of Kenneth Forbus, Patrick Hayes and Jerry Hobbs.

structures, or interpretations, in the sense of first-order logic. In C+, on the other hand, a state is an interpreta-.

This article is the basis of an invited talk at KR-96 in 1996 November. It has been modified from the version that appeared in the preprints of that meeting. There is an html version, a.dvi version,.pdf version and a.ps version. Up to: Main McCarthy page Up to: Send comments to mccarthy @stanford.edu. I sometimes make changes suggested in them. - John McCarthy.