![]() de Wit, Vincent ![]() in IfCoLog Journal of Logics and Their Applications (2023) In this article, we present a proof-theoretical and model-theoretical approach to probabilistic logic for reasoning about uncertainty about normative state- ments. We introduce two logics with languages ... [more ▼] In this article, we present a proof-theoretical and model-theoretical approach to probabilistic logic for reasoning about uncertainty about normative state- ments. We introduce two logics with languages that extend both the language of monadic deontic logic and the language of probabilistic logic. The first logic allows statements like “the probability that one is obliged to be quiet is at least 0.9”. The second logic allows iteration of probabilities in the language. We axiomatize both logics, provide the corresponding semantics and prove that the axiomatizations are sound and complete. We also prove that both logics are decidable. In addition, we show that the problem of deciding satisfiability for the simpler of our two logics is in PSPACE, no worse than that of deontic logic. [less ▲] Detailed reference viewed: 38 (6 UL)![]() ; ; van der Torre, Leon ![]() in Artificial Intelligence and Law (2020), 283 In this paper we address the interplay among intention, time, and belief in dynamic environments. The first contribution is a logic for reasoning about intention, time and belief, in which assumptions of ... [more ▼] In this paper we address the interplay among intention, time, and belief in dynamic environments. The first contribution is a logic for reasoning about intention, time and belief, in which assumptions of intentions are represented by preconditions of intended actions. Intentions and beliefs are coherent as long as these assumptions are not violated, i.e. as long as intended actions can be performed such that their preconditions hold as well. The second contribution is the formalization of what-if scenarios: what happens with intentions and beliefs if a new (possibly conflicting) intention is adopted, or a new fact is learned? An agent is committed to its intended actions as long as its belief-intention database is coherent. We conceptualize intention as commitment toward time and we develop AGM-based postulates for the iterated revision of belief-intention databases, and we prove a Katsuno-Mendelzon-style representation theorem. [less ▲] Detailed reference viewed: 73 (2 UL) |
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