Showing papers on "Normal modal logic published in 1986"

A framework for intuitionistic modal logics: extended abstract

Abstract: This abstract presents work on a Kripkean analysis of intuitionistic modal logic. As remarked in [BS] there ought to be such a subject, but in fact there is very little literature [B1, B2, F1, F2, V1, V2, V3]. One possible explanation is simply that it is hardly obvious what the applications would be. It seems to us however that there is a wide range of computational applications and indeed so many are the possibilities that it is worth beginning by sorting out the basic theory.

MOLOG: A system that extends PROLOG with modal logic

Abstract: In this paper we present an extension of PROLOG using modal logic. A new deduction method is also given based on a rule closer to the classical inference rule of PROLOG.

Modal Theorem Proving

Abstract: We describe resolution proof systems for several modal logics. First we present the propositional versions of the systems and prove their completeness. The first-order resolution rule for classical logic is then modified to handle quantifiers directly. This new resolution rule enables us to extend our propositional systems to complete first-order systems. The systems for the different modal logics are closely related.

Modality and Possibility in Some Intuitionistic Modal Logics

Abstract: «-> -1Λ/-1. However if we work on anintuitionistic nonmodal base logic, then some properties of the negation areweakened, the duality disappears, and it is commonly admitted that both equiv-alences cannot remain valid, because they lead to conclusions stronger thanwished (see [4]). Of course one could ignore one of the two modal operators,but we think this pointless, because the dual interpretation of one of them givesnatural birth to the other one.

A resolution method for quantified modal logics of knowledge and belief

Abstract: B-resolution is a sound and complete resolution rule for quantified modal logics of knowledge and belief with a standard Kripke semantics. It differs from ordinary first-order binary resolution in that it can have an arbitrary (but finite) number of inputs, is not necessarily effective, and does not have a most general unifier covering every instance of an application. These properties present obvious obstacles to implementation in an automatic theorem-proving system. By using a technique similar to semantic attachment, we obtain a very natural expression of B-resolution that is potentially efficient, and easily understood and controlled. We have implemented the method and used it to solve the Wise Man Puzzle.

Resolution and quantified epistemic logics

Abstract: Quantified modal logics have emerged as useful tools in computer science for reasoning about knowledge and belief of agents and systems. An important class of these logics have a possible-world semantics from Kripke. Surprisingly, there has been relatively little work on proof theoretic methods that could be used in automatic deduction systems, although decision procedures for the propositional case have been explored. In this paper we report some general results in this area, including completeness, a Herbrand theorem analog, and resolution methods. Although they are developed for epistemic logics, we speculate that these methods may prove useful in quantified temporal logic also.

Modal logics with several operators and provability interpretations

Abstract: The results herein solve positively some conjectures of Smorynski by generalizing results of Solovay (1976). The proofs rest on a modification of the usual semantics for modal logic and Solovay’s techniques.

On modal logics axiomatizing provability

Abstract: On the basis of the concept of the trace of a modal logic, introduced earlier by the author, a classification of arithmetically complete modal logics is given. It is proved that, between the least and the greatest arithmetically complete logics, there are continuum many logics which are not arithmetically complete. Bibliography: 19 titles.

Programming in Modal Logic: An Extension of PROLOG based on Modal Logic

Abstract: In this paper, we will attempt to give a procedural interpretation to modal logic. Modal logic is used as a programming language and then its procedural interpretation defines a computational procedure for the language. This is done within the framework of logic programming and is one of extensions of PROLOG based on modal logic. Further, we will demonstrate some advantages of the extension such as modurality, hierarchy or structure of logic programs.

Some results on dyadic deontic logic and the logic of preference

Abstract: Broadly conceived, deontic logic is the logical study of the normative use of language and its subject matter consists of a variety of normative concepts, notably those of obligation (prescription), prohibition (forbiddance), permission and commitment. A powerful trend of research in the area was initiated by the famous contribution von Wright (1951), where the formal properties of monadic (\"unconditional\", \"absolute\") normative concepts were systematically explored. Certain paradoxical results were seen to arise in von Wright's monadic deontic logic, however, which led him to propose systems for dyadic (\"conditional\", \"relative\") normative notions, where the concepts of obligation, permission etc., are made relative to, or conditional on certain circumstances. Thus, the dyadic deontic logic of von Wright (1956) was proposed as a reaction to the Prior (1954) Paradoxes of Commitment (\"derived obligation\"), and that of von Wright (1964) and (1965) as a reaction to the Chisholm (1963) Contrary-to-Duty Imperative Paradox. Our main concern in this paper will be certain later developments of dyadic deontic logic, which are characterized by the endeavor to relate the subject to Preference Theory in some way or other. A preference-theoretical approach to the problems of dyadic deontic logic was proposed by several writers in the late sixties and the early seventies. Pioneering contributions are Sven Danielsson (1968) and Bengt Hansson (1969), followed, e.g., by Bas C. van Fraassen (1972), David Lewis (1974) and Franz von Kutschera (1974). In section 2 below we present the language, syntax, proof-theory and the semantics of an axiomatic system G, which arose as a result of my attempt to reconstruct and to generalize the Hansson (1969) systems of dyadic standard deontic logic; see Aqvist (1984, Chap. VI, §§22-24), G may be said to codify a Hansson-von Kutschera-Aqvist line of interpreting the basic pair O, P of dyadic deontic operators. There is another line of interpreting them, though, which I'd like to call the Danielssonvan Fraassen-Lewis one. From the standpoint of our system G we can