Modal operator

About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.

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.

Reasoning about epistemic states of agents by modal logic programming

Abstract: Modal logic programming is one of appropriate approaches to deal with reasoning about epistemic states of agents. We specify here the least model semantics, the fixpoint semantics, and an SLD-resolution calculus for modal logic programs in the multimodal logic KD4I g 5 a , which is intended for reasoning about belief and common belief of agents. We prove that the presented SLD-resolution calculus is sound and complete. We also present a formalization of the wise men puzzle using a modal logic program in KD4I g 5 a . This shows that it is worth to study modal logic programming for multi-agent systems.

Extracting Non-Deterministic Concurrent Programs.

Abstract: We introduce an extension of intuitionistic fixed point logic by a modal operator facilitating the extraction of non-deterministic concurrent programs from proofs. We apply this extension to program extraction in computable analysis, more precisely, to computing with Tsuiki's infinite Gray code for real numbers.

Three-Valued Modal Logic for Qualitative Comparative Policy Analysis with Crisp-Set QCA

Abstract: Contradictory and missing outcomes are problems common to many qualitative comparative studies, based on the methodology of crisp-set QCA. They also occur in public policy analyses, e.g. if important background variables are omitted or outcomes of new policies are technically censored. As a new solution to these problems, this article proposes the use of three-valued modal logic, originally introduced by the Polish philosopher Jan Lukasiewicz (1970). In addition to true and false, indeterminate is the third truth-value in this alternative approach, which serves to code missing or contradictory data. Moreover, modal operators allow a differentiation between strict and possible triggers and inhibitors of policy outcomes. The advantages of three-valued modal logic in crisp-set QCA are illustrated by an empirical example from comparative welfare policy analysis. Its conclusions allow comparisons with the corresponding results from a conventional crisp-set QCA of the same data-set.

A Parallel Memory-efficient Epistemic Logic Program Solver: Harder, Better, Faster

Abstract: As the practical use of answer set programming (ASP) has grown with the development of efficient solvers, we expect a growing interest in extensions of ASP as their semantics stabilize and solvers supporting them mature. Epistemic Specifications, which adds modal operators K and M to the language of ASP, is one such extension. We call a program in this language an epistemic logic program (ELP). Solvers have thus far been practical for only the simplest ELPs due to exponential growth of the search space. We describe a solver that is able to solve harder problems better (e.g., without exponentially-growing memory needs w.r.t. K and M occurrences) and faster than any other known ELP solver.