相关论文: Kripke Completeness of Strictly Positive Modal Log…

We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the…

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…

In this paper, we investigate arithmetical completeness with respect to finite Kripke models of quantified modal logic. We adapt the finite-model embedding techniques of Artemov and Japaridze to two settings involving finite Kripke models.…

The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on…

We study fixpoints of operators on lattices. To this end we introduce the notion of an approximation of an operator. We order approximations by means of a precision ordering. We show that each lattice operator O has a unique most precise or…

We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…

The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which…

There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the…

The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely…

We present a clausal resolution-based method for normal multimodal logics of confluence, whose Kripke semantics are based on frames characterised by appropriate instances of the Church-Rosser property. Here we restrict attention to eight…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal…

In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…

The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…

We investigate preservation results for the independent fusion of one-variable first-order modal logics. We show that, without equality, Kripke completeness and decidability of the global and local consequence relation are preserved, under…

We study the completeness problem for propositionally quantified modal logics on quantifiable general frames, where the admissible sets are the propositions the quantifiers can range over and expressible sets of worlds are admissible, and…

It is known that not only classical semantics but also intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth tables, or truth functions. In our previous work, it…

We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…

This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the…