This chapter begins with a discussion of Indian theories of inference. It identifies the unique features of Indian logic not found in Western logic. Indian theories of inference are primarily theories of adequate evidence, but they may also be viewed as systems of nonmonotonic reasoning, which is being used in modern computer simulation of actual human reasoning processes. The chapter then discusses Nyāya logic, Buddhist logic, Jaina logic, and Navya–Nyāya logic.

My chief aim has been to convey the thought that the application of model theoretic techniques to natural languages needn't force a distortion of intentional phenomena. I hope that at least I have succeeded in accomplishing this.

inheritance reasoning in semantic networks allowing for multiple inheritance with exceptions. The approach leads to a definition of iaheritance that is..

Early attempts at combining multiple inheritance with nonmonotonic reasoning were based on straightforward extensions of tree-structured inheritance systems, and were theoretically unsound. In The Mathcmat~'cs of Inheritance Systcrns, or TMOIS, Touretzky described two problems these systems cannot handle: reasoning in the presence of true but redundant assertions, and coping with ambiguity. TMOIS provided a definition and analysis of a theoretically sound multiple inheritance system, accom-.

For as long as there have been theories about common knowledge, they have been exposed to a certain amount of skepticism. Recent more sophisticated arguments question whether agents can acquire common attitudes and whether they are needed in social reasoning. I argue that this skepticism arises from assumptions about practical reasoning that, considered in themselves, are at worst implausible and at best controversial. A proper approach to the acquisition of attitudes and their deployment in decision making leaves room for common (...) attitudes. Postulating them is no worse off than similar idealizations that are usefully made in logic and economics. (shrink)

We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly (...) accepted methods for dealing with the logical paradoxes. (shrink)

A propositional system of modal logic is second-order if it contains quantifiers ∀p and ∃p, which, in the standard interpretation, are construed as ranging over sets of possible worlds (propositions). Most second-order systems of modal logic are highly intractable; for instance, when augmented with propositional quantifiers, K, B, T, K4 and S4 all become effectively equivalent to full second-order logic. An exception is S5, which, being interpretable in monadic second-order logic, is decidable.

The interpretation of indirect discourse is one of the most persistent and pervasive themes in post-Fregean semantics. Since Frege we have managed to learn a good deal about the workings of various technical approaches to indirect discourse, but fundamental philosophical issues have remained unresolved.

This paper proposes a formalization of ability that is motivated in part by linguistic considerations and by the philosophical literature in action theory and the logic of ability, but that is also meant to match well with planning formalisms, and so to provide an account of the role of ability in practical reasoning. Some of the philosophical literature concerning ability, and in particular [Austin, 1956], suggests that some ways of talking about ability are context-dependent. I propose a way of formalizing (...) this dependency. (shrink)

The psychological orientation treats semantics as a matter of idealized computation over symbolic structures, and semantic relations like denotation as relations between linguistic expressions and these structures. I argue that results similar to Gödel's incompleteness theorems and Tarski's theorem on truth create foundational difficulties for this view of semantics.

We relate the theory of presupposition accommodation to a computational framework for reasoning in conversation. We understand presuppositions as private commitments the speaker makes in using an utterance but expects the listener to recognize based on mutual information. On this understanding, the conversation can move forward not just through the positive effects of interlocutors’ utterances but also from the retrospective insight interlocutors gain about one anothers’ mental states from observing what they do. Our title, ENLIGHTENED UPDATE, highlights such cases. Our (...) approach fleshes out two key principles: that interpretation is a form of intention recognition; and that intentions are complex informational structures, which specify commitments to conditions and to outcomes as well as to actions. We present a formalization and implementation of these principles for a simple conversational agent, and draw on this case study to argue that pragmatic reasoning is holistic in character, continuous with common-sense reasoning about collaborative activities, and most effectively characterized by associating specific, reliable interpretive constraints directly with grammatical forms. In showing how to make such claims precise and to develop theories that respect them, we illustrate the general place of computation in the cognitive science of language. (shrink)

The first amounts, roughly, to "It is necessarily the case that any President of the U.S. is a citizen of the U.S." But the second says, "the person who in fact is the President of the U.S, has the property of necessarily being a citizen of the U.S," Thus, while (2) is clearly true, it would be reasonable to consider (3) false.

This paper develops a general approach to contextual reasoning in natural language processing. Drawing on the view of natural language interpretation as abduction (Hobbs et al., 1993), we propose that interpretation provides an explanation of how an utterance creates a new discourse context in which its interpreted content is both true and promi- nent. Our framework uses dynamic theories of semantics and pragmatics, formal theories of context, and models of attentional state. We describe and illustrate a Prolog implementation.

rich domain involves an intricate mixture of strict and defeasible information. The importance of representing defeasible information in an inheritance system has been widely recognized, but it is not enough for a sys-.

This is part of a larger project that is motivated in part by linguistic considerations and by the philosophical literature in action theory and the logic of ability, but that is also meant to suggest ways in which planning formalisms could be modified to provide an account of the role of ability in planning and practical reasoning.

“Philosophy of action” is a recognized specialty in contemporary philosophy, and the literature on action is fairly extensive: see, for instance, (Care & Landesman 1968; Goldman 1970; Hornsby 1980). The relation of actions to their effects is formulated most clearly in the more specialized literature on the logic of action; see (Belnap & Perloff 1988; Chellas 1992; Czelakowski 1996; Segerberg 1982).

I believe that this approach leads to a wider problem that brings together elements of linguistics and philosophy in an illuminating way. But the single case study that I provide here, while it may be suggestive, does not go far enough to make a good case for the more general point. This paper is extracted from a larger collection of documents, and is intended to motivate and illustrate the ideas.

This article provides an overview of the subfield of Artificial Intelligence known as “Knowledge Representation and Reasoning.” This field uses the techniques of philosophical logic, but aims at providing a theoretical basis for the management of declarative information in automated reasoning systems. Three topics are singled out here for attention: planning and reasoning about actions, description logics, and nonmonotonic logics.