Showing papers on "Modal operator published in 1979"

First Order Theories of Individual Concepts and Propositions.

Abstract: We discuss rst order theories in which individual concepts are admitted as mathematical objects along with the things that reify them. This allows very straightforward formalizations of knowledge, belief, wanting, and necessity in ordinary rst order logic without modal operators. Applications are given in philosophy and in articial intelligence. We do not treat general concepts, and we do not present any full axiomatizations but rather show how various facts can be expressed.

The Modal Logic of Programs

Abstract: We explore the general framework of Modal Logic and its applicability to program reasoning. We relate the basic concepts of Modal Logic to the programming environment: the concept of "world" corresponds to a program state, and the concept of "accessibility relation" corresponds to the relation of derivability between states during execution. Thus we adopt the Temporal interpretation of Modal Logic. The variety of program properties expressible within the modal formalism is demonstrated.

Canonical modal logics and ultrafilter extensions

Abstract: In this paper the canonical modal logics, a kind of complete modal logics introduced in K Fine [4] and R I Goldblatt [5], will be characterized semantically using the concept of an ultrafilter extension, an operation on frames inspired by the algebraic theory of modal logic Theorem 8 of R I Goldblatt and S K Thomason [6] characterizing the modally definable Σ⊿-elementary classes of frames will follow as a corollary A second corollary is Theorem 2 of [4] which states that any complete modal logic defining a Σ⊿-elementary class of frames is canonicalThe main tool in obtaining these results is the duality between modal algebras and general frames developed in R I Goldblatt [5] The relevant notions and results from this theory will be stated in §2 The concept of a canonical modal logic is introduced and motivated in §3, which also contains the above-mentioned theorems In §4, a kind of appendix to the preceding discussion, preservation of first-order sentences under ultrafilter extensions (and some other relevant operations on frames) is discussedThe modal language to be considered here has an infinite supply of proposition letters (p, q, r, …), a propositional constant ⊥ (the so-called falsum, standing for a fixed contradiction), the usual Boolean operators ¬ (not), ∨ (or), ∨ (and), → (if … then …), and ↔ (if and only if)—with ¬ and ∨ regarded as primitives—and the two unary modal operators ◇ (possibly) and □ (necessarily)— ◇ being regarded as primitive Modal formulas will be denoted by lower case Greek letters, sets of formulas by Greek capitals

Local and global operators and many-valued modal logics.

Abstract: 1 Motivation In formal contexts, we may distinguish between two types of conditional operators.* The truth value of a local conditional is defined in terms of the truth values of its antecedent and consequent. The truth value of a global conditional is defined in terms of the possible truth-values of its antecedent and consequent. Global conditionals are usually formed by applying a modal operator to a local conditional. For example, strict implication is defined by applying the necessity operator to material implication. That is, \"p-$q\" is defined as \"L(p CO # ) \" , where CO is the standard two-valued material implication and the properties of the necessity operator \" L \" are determined by the particular modal logic being employed. There has been some move to formally treat ordinary language counterfactual conditionals as global conditionals of a certain sort. (See for example [1] and [3]). Viewed from this perspective, the local conditional involved is not the standard two-valued material implication, but is rather a three-valued operator. We may use Γ, F, and / for \" t r u e \" , \" fa lse\", and \"indeterminate\", respectively. We may then define the conditional Cl as follows (contrasting it with material implication CO):

Informational Independence in Intensional Context

Abstract: In his paper ‘Quantifiers vs. Quantification Theory’, Hintikka argues for the existence of partially ordered quantification in English.

Is the semantics of branching structures adequate for chronological modal logics

Abstract: In many important philosophical discussions we need a formal theory of tensed modalities or a combined modal and tense logic. As McArther (1976, Chapter 3), McKim and Davis (1976), Thomason (1970) and the like have argued, the semantics of branching structures is indeed adequate for many non-metric tense logics with modal operators like OT in the sense that semantical completeness can be established. Can we extend this semantical approach to metric tense logics with modal operators or, as I prefer to call them, chronological modal logics? In Nishimura (1979) we have already proved that the semantics of causal structures was indeed adequate for chronological modal logics. Causal structures may be called "parallel histories", "history-time index systems with the likeness relation", etc., if the reader wants to. Thus if we were able to prove the eqiiivalence of branching structures and causal structures, the adequacy of branching structures for chronological modal logics would follow immediately. Which semantics we should adopt be a matter of taste in this case.

On the non-availability of Dawson-modeling into certain relevance alethic modal logics

Abstract: This paper shows that the Dawson technique of modelling deontic logics into alethic modal logics to gain insight into deontic formulas is not available for modelling a normal (in the spirit of Anderson) relevance deontic modal logic into either of the normal relevance alethic modal logics R□ S4or R□ M. The technique is to construct an extension of the well known entailment matrix set M 0and show that the model of the deontic formula P (A v B)→. PA v PB is excluded.