Showing papers on "Normal modal logic published in 1983"

Proof Methods for Modal and Intuitionistic Logics

Abstract: One / Background.- Two / Analytic Modal Tableaus and Consistency Properties.- Three / Logical Consequence, Compactness, Interpolation, and Other Topics.- Four / Axiom Systems and Natural Deduction.- Five / Non-Analytic Logics.- Six / Non-Normal Logics.- Seven / Quantifiers.- Eight / Prefixed Tableau Systems.- Nine / Intuitionistic Logic.- Special Notation.

Permissions and obligations

Abstract: This article describes a formal semantics for the deontic concepts -- the concepts of permission and obligation -- which arises naturally from the representations used in artificial intelligence systems Instead of treating deontic logic as a branch of modal logic, with the standard possible worlds semantics, we first develop a language for describing actions, and we define the concepts of permission and obligation in terms of these action descriptions. Using our semantic definitions, we then derive a number of intuitively plausible inferences, and we show generally that the paradoxes which are so frequently associated with deontic logic do not arise in our system.

Algebraic semantics for quasi-classical modal logics

Abstract: A well-known result, going back to the twenties, states that, under some reasonable assumptions, any logic can be characterized as the set of formulas satisfied by a matrix 〈 , F 〉, where is an algebra of the appropriate type, and F a subset of the domain of , called the set of designated elements. In particular, every quasi-classical modal logic—a set of modal formulas, containing the smallest classical modal logic E , which is closed under the inference rules of substitution and modus ponens—is characterized by such a matrix, where now is a modal algebra, and F is a filter of . If the modal logic is in fact normal, then we can do away with the filter; we can study normal modal logics in the setting of varieties of modal algebras. This point of view was adopted already quite explicitly in McKinsey and Tarski [8]. The observation that the lattice of normal modal logics is dually isomorphic to the lattice of subvarieties of a variety of modal algebras paved the road for an algebraic study of normal modal logics. The algebraic approach made available some general results from Universal Algebra, notably those obtained by Jonsson [6], and thereby was able to contribute new insights in the realm of normal modal logics [2], [3], [4], [10]. The requirement that a modal logic be normal is rather a severe one, however, and many of the systems which have been considered in the literature do not meet it. For instance, of the five celebrated modal systems, S1–S5, introduced by Lewis, S4 and S5 are the only normal ones, while only SI fails to be quasi-classical. The purpose of this paper is to generalize the algebraic approach so as to be applicable not just to normal modal logics, but to quasi-classical modal logics in general.

On some proof theoretical properties of the modal logic GL

Abstract: This paper deals with the system of modal logicGL, in particular with a formulation of it in terms of sequents. We prove some proof theoretical properties ofGL that allow to get the cut-elimination theorem according to Gentzen's procedure, that is, by double induction on grade and rank.

Physicalism, instrumentalism and the semantics of modal logic

Abstract: The delicate point in the formalistic position is to explain how the non-intuitionistic classical mathematics is significant, after having initially agreed with the intuitionists that its theorems lack a real meaning in terms of which they are true (S. C. Kleene, 1952).

Compatible complement in Piron’s system and ordinary modal logic

Abstract: Previous critiques of the relevant of Piron’s questions-propositions system as a generated of quantum mechanics by interpretation are reinforced by confrontation with the de Morgan laws and with the ordinary modal logic.

Chang's modal operators in algebraic logic

Abstract: Chang algebras as algebraic models for Chang's modal logics [1] are defined. The main result of the paper is a representation theorem for these algebras.

A Cut-Free Sequential System for the Propositional Modal Logic of Finite Chains

Abstract: The main purpose of this paper is to give a cut-free Gentzen-type sequential system for K4.3G of finite chains. The cut-elimination theorem is proved both modeltheoretically and proof-theoretically.

Hauptsatz for Higher-Order Modal Logic

Abstract: In spite of the philosophical significance of higher-order modal logic, the modal logician's main concern has been with sentential logic. In this paper we do not intend to go into philosophical details, but we only remark that higher-order modal logic has a close relationship with Montague's well-known idea of “universal grammar”, which is an ambitious attempt to build a logical theory of natural languages with exact syntax and semantics, comparable with the artificial languages of mathematical logic. For this matter, the reader can consult, e.g., Montague [8], [9] and Gallin [2].

W-JS: a modal logic of knowledge

Abstract: W-JS is a first-order predicate calculus on the modal theory of knowledge. It is based on natural deduction rules and accompanied by possible-world-accessibility semantics. As an example, the famous "Mr. S and Mr. P" puzzle is solved in W-JS.

The modal logic of consistency assertions of peano arithmetic

Abstract: 8