Modal operator

About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.

Natural Deduction Based upon Strict Implication for Normal Modal Logics

Abstract: We present systems of Natural Deduction based on Strict Implication for the main normal modal logics between K and S5. In this work we consider Strict Implication as the main modal operator, and establish a natural correspondence between Strict Implication and strict subproofs.

Tableau Development for a Bi-intuitionistic Tense Logic

Abstract: The paper introduces a bi-intuitionistic logic with two modal operators and their tense versions. The semantics is defined by Kripke models in which the set of worlds carries a pre-order relation as well as an accessibility relation, and the two relations are linked by a stability condition. A special case of these models arises from graphs in which the worlds are interpreted as nodes and edges of graphs, and formulae represent subgraphs. The pre-order is the incidence structure of the graphs. These examples provide an account of time including both time points and intervals, with the accessibility relation providing the order on the time structure. The logic we present is decidable and has the effective finite model property. We present a tableau calculus for the logic which is sound, complete and terminating. The MetTel system has been used to generate a prover from this tableau calculus.

ON THE DIAGRAM OF ONE TYPE MODAL OPERATORS ON INTUITIONISTIC FUZZY SETS: LAST EXPANDING WITH Zω,θα,β

Abstract: Intuitionistic Fuzzy Modal Operator was defined by Atanassov in [3] in 1999. In 2001, [4], he introduced the generalization of these modal operators. After this study, in 2004, Dencheva [14] defined second extension of these operators. In 2006, the third extension of these was defined in [6] by Atanassov. In 2007,[11], the author introduced a new operator over Intuitionistic Fuzzy Sets which is a generalization of Atanassov’s and Dencheva’s operators. At the same year, Atanassov defined an operator which is an extension of all the operators defined until 2007. The diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets was introduced first in 2007 by Atanassov [10]. In 2008, Atanassov defined the most general operator and in 2010 the author expanded the diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets with the operator Zω α,β . Some relationships among these operators were studied by several researchers[5]-[8] [11], [13], [14][19]. The aim of this paper is to expand the diagram of one type modal operators over intuitionistic fuzzy sets . For this purpose, we defined a new modal oparator Z α,β over intuitionistic fuzzy sets. It is shown that this oparator is the generalization of the operators Zω α,β , Eα,β , α,β , α,β .

Modal nonmonotonic logics demodalized

Abstract: The study of the relation between default logic and modal nonmonotonic logics has been mostly concerned with the task of translating default logic to autoepistemic or some other modal nonmonotonic logic. Here, we discuss the reverse problem, that is, the possibility of translating modal nonmonotonic logics into default-type systems formulated in the language without modal operators. To this end, we first consider a reformulation of both formalisms in terms of what we call default consequence relations. These consequence relations turn out to be especially suitable for studying default and modal nonmonotonic reasoning. We show, in particular, that different kinds of such reasoning naturally correspond to different structural rules imposed on default consequence relations. Our main results also demonstrate that all modal nonmonotonic objects considered have exact nonmodal “counterparts”. As an immediate consequence of these results, we obtain a method of reducing common types of modal nonmonotonic reasoning to nonmodal default reasoning.

A General Framework for $$ {FDE}$$-Based Modal Logics

Abstract: We develop a general theory of FDE-based modal logics. Our framework takes into account the four-valued nature of FDE by considering four partially defined modal operators corresponding to conditions for verifying and falsifying modal necessity and possibility operators. The theory comes with a uniform characterization for all obtained systems in terms of FDE-style formula-formula sequents. We also develop some correspondence theory and show how Hilbert-style axiom systems can be obtained in appropriate cases. Finally, we outline how different systems from the literature can be expressed in our framework.