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.

Axioms for knowledge and time in distributed systems with perfect recall

Abstract: A distributed system, possibly asynchronous, is said to have perfect recall if at all times each processor's state includes a record of all its previous states. The completeness of a propositional modal logic of knowledge and time with respect to such systems is established. The logic includes modal operators for knowledge, and the linear time operators "next" and "until". >

Epistemic equilibrium logic

Abstract: We add epistemic modal operators to the language of here-and-there logic and define epistemic here-and-there models. We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from here-and-there models by the standard minimisation of truth of Pearce's equilibrium logic; they provide an epistemic extension of that logic. The latter are obtained from the former by maximising the set of epistemic possibilities; they provide a new semantics for Gelfond's epistemic specifications. For both definitions we characterise strong equivalence by means of logical equivalence in epistemic here-and-there logic.

Term-Modal Logics

Abstract: Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way. To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators. This gives us a flexible and uniform language for reasoning about the agents themselves and their knowledge. This article gives examples of the expressiveness of the languages and provides sequent-style and tableau-based proof systems for the logics. Furthermore we give proofs of soundness and completeness with respect to the possible world semantics.

A Logic of Knowing How

Abstract: In this paper, we propose a single-agent modal logic framework for reasoning about goal-direct “knowing how” based on ideas from linguistics, philosophy, modal logic and automated planning. We first define a modal language to express “I know how to guarantee ϕ given ψ” with a semantics not based on standard epistemic models but labelled transition systems that represent the agent’s knowledge of his own abilities. A sound and complete proof system is given to capture the valid reasoning patterns about “knowing how” where the most important axiom suggests its compositional nature.

15 Combining modal logics

Abstract: Publisher Summary This chapter surveys two key combination methods––namely, fusions and products. It also examines some other combination methods. The properties of combined logics depend on those of their components plus the particular method of combination. The idea of combining modal logics is natural for many applications. The chapter explores the way in which modal logics can be combined and highlights the consequences of combining them. The formation of fusions is the simplest and the most natural way of combining modal logics. The formation of Cartesian products of various structures—vector and topological spaces, algebras—is a standard mathematical way of capturing the multidimensional character of the world. In modal logic, products of Kripke frames are natural constructions allowing it to reflect interactions between modal operators representing time, space, knowledge, or actions. The product construction as a combination method on modal logics is introduced and is used in applications in computer science and artificial intelligence.