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.

Bringing about rationality: incorporating plans into a BDI agent architecture

Abstract: Agents attempt to achieve their intentions through the use of plans, leading to further intentions corresponding to the actions and subgoals of those plans We extend Rao and Georgeff's logic of belief, desire and intention with a logical representation of plans This representation allows the specification of subgoals, using Segerberg's "bringing it about" modal operator By using a plan library to semantically restrict an agent's intention-worlds, we define a framework that models the reasoning process of an intention-based autonomous agent We show that this framework supports several desirable properties involving an agent's commitment to future intentions, based on its available plans

ESmodels: An Epistemic Specification Solver.

Abstract: (To appear in Theory and Practice of Logic Programming (TPLP)) ESmodels is designed and implemented as an experiment platform to investigate the semantics, language, related reasoning algorithms, and possible applications of epistemic specifications.We first give the epistemic specification language of ESmodels and its semantics. The language employs only one modal operator K but we prove that it is able to represent luxuriant modal operators by presenting transformation rules. Then, we describe basic algorithms and optimization approaches used in ESmodels. After that, we discuss possible applications of ESmodels in conformant planning and constraint satisfaction. Finally, we conclude with perspectives.

First Steps in Synthetic Guarded Domain Theory.

Abstract: We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms, predicates, and types. In particular, we show how to solve recursive type equations involving dependent types. We propose that the internal logic of S provides the right setting for the synthetic construction of abstract versions of step-indexed models of programming languages and program logics. As an example, we show how to construct a model of a programming language with higher-order store and recursive types entirely inside the internal logic of S. Moreover, we give an axiomatic categorical treatment of models of synthetic guarded domain theory and prove that, for any complete Heyting algebra A with a well-founded basis, the topos of sheaves over A forms a model of synthetic guarded domain theory, generalizing the results for S.

Topos Semantics for Higher-Order Modal Logic

Abstract: We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E. In contrast to the well-known in- terpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the subobject classifier E, but rather by a suit- able complete Heyting algebra H. The canonical map relating H and E both serves to interpret equality and provides a modal operator on H in the form of a comonad. Examples of such structures arise from surjec- tive geometric morphisms f : F → E, where H = f∗F. The logic differs from non-modal higher-order logic in that the principles of functional and propositional extensionality are not longer valid but may be replaced by modalized versions. The usual Kripke, neighborhood, and sheaf seman- tics for propositional and first-order modal logic are subsumed by this notion.