Related papers: Modelling competing theories
We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible…
This paper continues the investigation of the logic of competing theories, be they scientific, social, political etc. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of…
We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each…
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…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
Multi-valued logical models can be used to describe biological networks on a high level of abstraction based on the network structure and logical parameters capturing regulatory effects. Interestingly, the dynamics of two distinct models…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
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…
The paper is dedicated to the problem of adding a modality to the \Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We investigate the expressive power of a Turing-complete logic based on game-theoretic semantics. By defining suitable fragments and variants of the logic, we obtain a range of natural characterizations for some fundamental families of…
In this paper, we further develop the framework of Modular Systems that lays model-theoretic foundations for combining different declarative languages, agents and solvers. We introduce a multi-language logic of modular systems. We define…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
Characterizations of semi-stable and stage extensions in terms of 2-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming…
This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice,…