Studia Logica 66 (1):79-119 (2000)

Wiebe Van Der Hoek
University of Liverpool
We demonstrate ways to incorporate nondeterminism in a system designed to formalize the reasoning of agents concerning their abilities and the results of the actions that they may perform. We distinguish between two kinds of nondeterministic choice operators: one that expresses an internal choice, in which the agent decides what action to take, and one that expresses an external choice, which cannot be influenced by the agent. The presence of abilities in our system is the reason why the usual approaches towards nondeterminism cannot be used here. The semantics that we define for nondeterministic actions is based on the idea that composite actions are unravelled in the strings of atomic actions and tests that constitute them. The main notions used in defining this semantics are finite computation sequences and finite computation runs of actions. The results that we obtain meet our intuitions regarding events and abilities in the presence of nondeterminism.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/A:1026796912842
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References found in this work BETA

Dynamic Logic.Lenore D. Zuck & David Harel - 1989 - Journal of Symbolic Logic 54 (4):1480.
Intention is Choice with Commitment.Philip R. Cohen & Hector J. Levesque - 1990 - Artificial Intelligence 42 (2-3):213-261.
On the Logic of Ability.Mark A. Brown - 1988 - Journal of Philosophical Logic 17 (1):1 - 26.

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