Showing papers on "Normal modal logic published in 1982"
TL;DR: The operator M (usually read "possible") is extended so that Mp is true whenever p is consistent with the theory, and any theorem of this form may be mvahdated if ~p ~s is added as an axiom.
Abstract: Tradmonal logics suffer from the "monotomclty problem"' new axioms never mvahdate old theorems One way to get nd of this problem ts to extend traditional modal logic in the following way The operator M (usually read "possible") is extended so that Mp is true whenever p is consistent with the theory Then any theorem of this form may be mvahdated if ~p ~s added as an axiom This extension results m nonmonotomc versions of the systems T, $4, and $5 These systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all "noncommittal" models of that theory, where a noncommittal model ts one m which as many thmgs are possible as possible Nonmonotomc $4 is probably the most interesting of the three, since it is stronger than ordinary $4 but has all the usual inferential machinery of $4 There is a straightforward proof procedure for the sententlal subset of nonmonotomc $4. This approach to nonmonotonlc logic may be applied to several problems in knowledge representation for arUficml mtelhgence Its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol M to appear m any context, since M is a meaningful part of the language
434 citations
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TL;DR: The main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes, together with a semantic framework provided by such a general notion of non-normal world.
Abstract: One way to obtain a comprehensive semantics for various systems of modal logic is to use a general notion of non-normal world. In the present article, a general notion of modal system is considered together with a semantic framework provided by such a general notion of non-normal world. Methodologically, the main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes. Some specific systems are studied together with semantics using non-normal worlds of different kinds.
40 citations
TL;DR: The axiomatization of the modal propositional system K is obtained by adding to the habitual formalization of that system the following axiom scIleme and the inference rule:.
40 citations
TL;DR: In the past two decades considerable energy and effort have been expended in the study of quantified modal logic, and many different systems have been developed including those given by Kripke in and Hughes and Cresswell in.
Abstract: In the past two decades considerable energy and effort have been expended in the study of quantified modal logic. The first formal semantics and completeness theorem were published by Kripke in 1959 [2], Since then, many different systems have been developed including those given by Kripke in [3] and Hughes and Cresswell in [ 1 ]. In each case the central informal idea underlying the formal semantics is the notion of possible world, a total way things could have been. Formally, a model structure for a first-order language L is a quadruple (D, W, φ, φ) such that:
27 citations
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TL;DR: In this paper, the question whether these paradoxes depend essentially on the use of classical logic and whether they can be avoided by using intuitionistic or minimal logic is considered, and the results show that intuitionistic logic is more efficient than minimal logic.
Abstract: Investigations in meta-theoretical topics such as the definability of disposition terms or the explication of qualitative and quantitative concepts of confirmation, as well as discussions of various systems of modal logic, e.g., deontic logic, often deal with a number of well known paradoxes. In general, classical logic is used in deriving the paradox of the ravens, Goodman's paradox, the paradoxes of derived obligation, etc. The questions whether these paradoxes depend essentially on the use of classical logic and whether they can be avoided by using intuitionistic or minimal logic are considered.
3 citations