Studia Logica 102 (3):441-478 (2014)

Abstract
We present a Hilbert style axiomatization and an equational theory for reasoning about actions and capabilities. We introduce two novel features in the language of propositional dynamic logic, converse as backwards modality and abstract processes specified by preconditions and effects, written as \({\varphi \Rightarrow \psi}\) and first explored in our recent paper (Hartonas, Log J IGPL Oxf Univ Press, 2012), where a Gentzen-style sequent calculus was introduced. The system has two very natural interpretations, one based on the familiar relational semantics and the other based on type semantics, where action terms are interpreted as types of actions (sets of binary relations). We show that the proof systems do not distinguish between the two kinds of semantics, by completeness arguments. Converse as backwards modality together with action types allow us to produce a new purely equational axiomatization of Dynamic Algebras, where iteration is axiomatized independently of box and where the fixpoint and Segerberg induction axioms are derivable. The system also includes capabilities operators and our results provide then a finitary Hilbert-style axiomatization and a decidable system for reasoning about agent capabilities, missing in the KARO framework
Keywords Logic of agency  Logic of capabilities  Dynamic logic of action types  Converse as backwards possibility
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DOI 10.1007/s11225-013-9473-8
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References found in this work BETA

Editorial.Wiebe van der Hoek - 2004 - Synthese 139 (2):133-134.
Reasoning About Types of Action and Agent Capabilities.C. Hartonas - 2013 - Logic Journal of the IGPL 21 (5):703-742.
Editorial.W. van der Hoek - 2003 - Logic Journal of the IGPL 11 (2):133-133.
Editorial.Wiebe van der Hoek & Michael Wooldridge - 2003 - Logic Journal of the IGPL 11 (2):133-134.

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