Related papers: Modal weak Kleene logics: axiomatizations and rela…
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 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…
Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by replacing the…
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…
This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have…
In this paper we develop a 2-valued reduction of many-valued logics, into 2-valued multi-modal logics. Such an approach is based on the contextualization of many-valued logics with the introduction of higher-order Herbrand interpretation…
A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always…
A three-valued logic L is subclassical when it is defined by a single matrix having the classical two-element matrix as a subreduct. In this case, the language of L can be expanded with special unary connectives, called external operators.…
Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some…
In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new \emph{binary} sequent calculi (each sequent is a pair of formulae) for…
Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete…
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 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…
Most non-classical logics are subclassical, that is, every inference/theorem they validate is also valid classically. A notable exception is the three-valued propositional Logic of Ordinary Discourse (OL) proposed and extensively motivated…
This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…
We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…
Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…