We study a modal language for negative operators —an intuitionistic-like negation and its paraconsistent dual— added to (bounded) distributive lattices. For each non-classical negation an extra operator is hereby adjoined in order to allow for standard logical inferences to be opportunely restored. We present abstract characterizations and exhibit the main properties of each kind of negative mo...

The LA-logics (“logics with Local Agreement”) are polymodal logics defined semantically such that at any world of a model, the sets of successors for the different accessibility relations can be linearly ordered and the accessibility relations are equivalence relations. In a previous work, we have shown that every LA-logic defined with a finite set of modal indices has an NP-complete satisfiabi...

Kripke semantics plays a fundamental role for modal logics where it often provides modular semantics allowing a clear treatment of various logics related by the addition of axioms or connectives. Kripke semantics is also the “natural semantics” for classical modal logic in the sense that it is given by the representation theory for modal algebras. The algebraic structure corresponding to a trad...

Ordinary linear implication can represent unconstrained state transition, but stateful systems often operate under temporal and stochastic constraints which impede the use of linear logic as a framework for representing stateful computations. We propose a general modal extension of linear logic where the worlds represent the constraints, and hybrid connectives combine constraint reasoning with ...

Deciding whether a modal formula is satisfiable with respect to a given set of (global) assumptions is a question of fundamental importance in applications of logic in computer science. Tableau methods have proved extremely versatile for solving this problem for many different individual logics but they typically do not meet the known complexity bounds for the logics in question. Recently, it h...

Enabling reasoning as simulations with concrete objects and relations has a merit of grounding reasoning to more basic perceptual mechanisms. In a hybrid artificial intelligence architecture that uses both logical and non-logical computational methods, the use of simulations for enabling logical inferences allows one to alternate between the logical method and a non-logical one that uses, for e...

Logical connectives familiar from the study of hybrid logic can be added to the logical framework LF, a constructive type theory of dependent functions. This extension turns out to be an attractively simple one, and maintains all the usual theoretical and algorithmic properties, for example decidability of type-checking. Moreover it results in a rich metalanguage for encoding and reasoning abou...

In this paper, we present a resolution calculus for the first-order modal logic S4. The formulas are given not necessary in a clausal form. This method can be used for automatizable proof procedure of a quantified modal logic. We will consider formulas for which the following conditions hold: 1. the formulas F contain only logical connectives ¬,&,∨, and no logical or modal symbol in F lies in t...

Modal fuzzy logics is a research topic that has attracted increasing attention in the last years. Several papers have been published treating different aspects, see for instance [6] for a modal expansion of Lukasiewicz logic, [3, 4, 2] for modal expansions of Gödel fuzzy logic, [1] for modal logics over finite residuated lattices, and more recently [7] for a modal expansion of Product fuzzy log...

We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4 and S5, such logics are useful, as shown in previous work by Baltag, Coecke and the first au...