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.

Logical Consequence in Modal Logic: Alternative Semantic Systems for Normal Modal Logics

Abstract: Publisher Summary This chapter discusses the alternative semantic systems of normal modal logics. The novelty of the approach discussed in the chapter is twofold: first, to treat modal logics as consequence systems rather than logistic systems; and second, to view modal logics as extensions of non-modal ones. This second feature leads to the realization that certain usually desired properties of modal logics (e.g., compactness, weak completeness, and strong completeness) are at least in part determined by properties of the semantic systems of their non-modal “base.”

Cover Systems for the Modalities of Linear Logic

Abstract: Ono's modal FL-algebras are models of an extension of Full Lambek logic that has the modalities ! and ? of linear logic Here we define a notion of modal FL-cover system that combines aspects of Beth-Kripke-Joyal semantics with Girard's interpretation of the ! modality, and has structured subsets that interpret propositions We show that any modal FL-algebra can be represented as an algebra of propositions of some modal FL-cover system

STIT Based Deontic Logics for the Miners Puzzle

Abstract: In this paper we first develop two new STIT based deontic logics capable of solving the miners puzzle. The key idea is to use pessimistic lifting to lift the preference over worlds into the preference over sets of worlds. Then we also discuss a more general version of the miners puzzle in which plausibility is involved. In order to deal with the more general puzzle we add a modal operator representing plausibility to our logic. Lastly we present a sound and complete axiomatization.

A Temporal-Logic Approach to Functional Calculi for Dependent Types and Higher-Order Encodings

Abstract: Dependent-types and higher-order encodings lead to concise and elegant representations of complex data structures as evidenced by the success of the logical framework LF [HHP93]. In this work we first design a functional calculus utilizing LF to represent its data objects. To avoid problems commonly associated with using the same function space for both representation (LF objects) and computation, we separate the two as influenced by our previous work [Sch05]. We then exploit the power of the past time connective from temporal logic to design a meta-logic to reason about higherorder abstract syntax. Sample programs that we discuss in this paper include bracket abstraction and a theorem prover. It is important to note that this technical report is an enhancement/ simplification of a previous technical report [Pos06] where past-time was used as a modal operator in the meta-logic for LF. Here, we use past-time on the meta-meta-level for LF.

On the semilattice of modal operators and decompositions of the discriminator

Abstract: We investigate the join semilattice of modal operators on a Boolean algebra B. Furthermore, we consider pairs \(\langle f,g \rangle \) of modal operators whose supremum is the unary discriminator on B, and study the associated bi-modal algebras.