Showing papers on "Normal modal logic published in 1976"

Provability interpretations of modal logic

Abstract: We consider interpretations of modal logic in Peano arithmetic (P) determined by an assignment of a sentencev * ofP to each propositional variablev. We put (⊥)*=“0 = 1”, (χ → ψ)* = “χ* → ψ*” and let (□ψ)* be a formalization of “ψ)* is a theorem ofP”. We say that a modal formula, χ, isvalid if ψ* is a theorem ofP in each such interpretation. We provide an axiomitization of the class of valid formulae and prove that this class is recursive.

Expressive completeness in modal language

Abstract: The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I think that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worlds

Methods for Automated Theorem Proving in Nonclassical Logics

Abstract: In this paper we outline two basic methods for automated theorem proving in nonclassical logics, including modal, many-valued, relevance, and intuitionistic logics We discuss advantages and disadvantages of each method and give several illustrative examples We outline a procedure for attacking more complex problems using a combination of the two basic methods Results of experimental applications of the techniques are reported

Aristotle's response to Quine's objections to modal logic

Abstract: In Section II it is shown that some of the Quinean objections to modal logic found in [ 151 can be transferred to the notions used to describe and account for temporal change.’ The remainder of the paper is devoted to a demonstration of the thesis that Aristotle’s predecessors had already formulated problems similar to the temporal puzzles so generated, and that the three most prominent reactions to Qume’s puzzles were also anticipated by certain ancient Greek philosophers. Furthermore, Aristotle’s own reaction as manifested in his analysis of the elements of change in Physics A7 can be seen to involve concepts which easily lend themselves to the kind of semantical analysis which has recently enhanced our understanding of modality. Let us begin, then, by getting clear on just what problems I have in mind.

A Partial Formalization of Kant’s Categorical Imperative. An Application of Deontic Logic to Classical Moral Philosophy

Abstract: Kant's criterion of morality, the categorical Imperative, is usually described äs a \"formal\" criterion — in contradistinction to other criteria whidi are more \"substansive\". Now, this characterization of Kant's Imperative should be a challenge for philosophical logicians. If this renowned criterion is really \"formal\" — why not formalize it? Obviously, a formalization of Kant's Imperative is possible only when an appropriate formal framework is available. Quantification theory is not an appropriate System, since the concepts of \"Obligation\" and \"Permission\" which are essential to any formalization of a moral criterion are not among its logical constants. On the other hand, a variety of deontic logics have been developed