Topic
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.
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TL;DR: An extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ⋄φ expresses that there is a truthful announcement φ after which φ is true.
Abstract: Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ♦ϕ expresses that there is a truthful announcement ψ after which ϕ is true. This logic gives a perspective on Fitch’s knowability issues: for which formulas ϕ does it hold that ϕ → ♦Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.
134 citations
TL;DR: This paper proposes an extension of the simply typed lambda-calculus with iteration and case constructs which preserves the adequacy of higher-order abstract syntax encodings, and views the methodology of LF to be employed effectively in systems based on induction principles, leading to a synthesis of currently incompatible paradigms.
130 citations
TL;DR: In this article, the authors consider modal languages with a modal operator D whose semantics is based on the relation of inequality, and some connections with a number of other recent proposals to extend the standard modal language are pointed out.
Abstract: We consider some modal languages with a modal operator D whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at.
129 citations
26 May 2004
TL;DR: This paper studies the logic of a dyadic modal operator for being obliged to meet a condition ρ before a condition δ becomes true, and shows that this notion of deadline obligation can be characterized in the branching time logic CTL.
Abstract: This paper studies the logic of a dyadic modal operator for being obliged to meet a condition ρ before a condition δ becomes true. Starting from basic intuitions we arrive at a simple semantics for deadline obligations in terms of branching time models. We show that this notion of deadline obligation can be characterized in the branching time logic CTL. The defined operator obeys intuitive logic properties, like monotony w.r.t. ρ and anti-monotony w.r.t. δ, and avoids some counter-intuitive properties like agglomeration w.r.t ρ and’weak agglomeration’ w.r.t. δ. However, obligations of this type are implied by the actual achievement of ρ before the deadline. We argue that this problem is caused by the fact that we model the obligation only from the point of view of its violation conditions. We show that the property might be eliminated by considering success conditions also.
124 citations
TL;DR: A methodology for the verification of multi-agent systems, whose properties are specified by means of a modal logic that includes a temporal, an epistemic, and amodal operator to reason about correct behaviour of agents.
121 citations