A. An intuitionistic, hybrid modal logic suitable for reasoning about distribution of resources was introduced in [10]. We extend the Kripke semantics of intuitionistic logic, enriching each possible Kripke state with a set of places, and show that this semantics is both sound and complete for the logic. In the semantics, resources of a distributed system are interpreted as atoms, and pl...

The Logic of Epistemic Actions and Knowledge (EAK) has been introduced by Baltag, Moss and Solecki [1] as a framework for reasoning about knowledge in a dynamic setting. It is thus a language expansion of (classical) modal logic having, besides the usual modal operators that represent knowledge and beliefs of agents, dynamic operators used to represent the epistemic change that can be brought a...

Modal dependence logic was introduced recently by Väänänen. It enhances the basic modal language by an operator =(). For propositional variables p1, . . . , pn, =(p1, . . . , pn−1, pn) intuitively states that the value of pn is determined by those of p1, . . . , pn−1. Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministi...

We investigate the proof theory of a modal fragment of XPath equipped with data (in)equality tests over finite data trees, i.e. over finite unranked trees where nodes are labelled with both a symbol from a finite alphabet and a single data value from an infinite domain. We present a sound and complete sequent calculus for this logic, which yields the optimal PSPACE complexity bound for its vali...

As an extension of the traditional modal logic, the fuzzy first-order modal logic is discussed in this paper. A description of fuzzy first-order modal logic based on constant domain semantics is given, and a formal system of fuzzy reasoning based on the semantic information of models of first-order modal logic is established. It is also introduced in this paper the notion of the satisfiability ...

The nondeterministic information logic NIL has been introduced by Or lowska and Pawlak in 1984 as a logic for reasoning about total information systems with the similarity, the forward inclusion and the backward inclusion relations. In 1987, Vakarelov provides the first first-order characterization of structures derived from information systems and this has been done with the semantical structu...

Basic propositional logic was first introduced by Albert Visser in [6]. Basic logic is a proper subsystem of intuitionistic logic, and can be constructed from it by a weakening of modus ponens. This weakening allows for a larger collection of theories, for example formal provability logic. Formal provability logic is related to the provability modal logic GL just as intuitionistic logic is rela...

This paper, a sequel to "Models for normal intuitionistie modal logics" by M. Bo~i6 and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of $4 and $5. For these propositional logics Kripke-style models with two accessibility relations, one intuitionistic and the ot...

In this paper we extend the basic principles and results of conservative logic to include the main features of many-valued logics with a finite number of truth values. Different approaches to many-valued logics are examined in order to determine some possible functionally complete sets of logic connectives. As a result, we describe some possible finite-valued universal gates which realize a fun...

Modal Logic is traditionally concerned with the intensional operators “possibly” and “necessary”, whose intuitive correspondence with the standard quantifiers “there exists” and “for all” comes out clearly in the usual Kripke semantics. This observation underlies the well-known translation from propositional modal logic with operators ♦ and , possibly indexed, into the first-order language over...