quinta-feira, 27 de outubro de 2011

Seminário do Grupo de Lógica, Inteligência Artificial e Métodos Formais - LIAMF: "Interactions Between (Modal) Logics and Probability" de Marcelo Finger

Local: Sala 256A, Bloco A do IME-USP
Data: quinta-feira, 27/10/2011 às 14h

Resumo: There are several points in common between modal logics and probabilistic logic. The semantics of modal logics is given in terms of possible worlds, and the semantics of probabilistic logics assigns a probability distribution to a set of possible worlds as well. So we study that relationship in detail. We start by present a particular modal logic that captures the notion of probabilistic entailment in a setting free of independence pressupositions, an show it respects Kolmogorov's probability axioms. It turns out that a decision procedure for this logic-probabilistic entailment is "only" NP-complete and can serve as a basis for logic-probabilistic abduction. Then we examine a modal logic that deals with conditional probabilities. This is somewhat challenging, due to a famous result by D. Lewis [1973] which shows that a logic that has conditional probabilities with very basic properties and respects Kolmogorov is forced to get to some "trivializations" results. However, we formulate one such conditional probabilistic modal logic system and show Kolmogorov axioms can be simply adapted not to lead to trivializations. This system has an intrinsic interest in itself, for it imposes some context-sensitivity to a logic, a fact very rarely found in logic systems.


Seminário Registrado na CPG do IME/USP
Página: http://www.ime.usp.br/~liamf/seminarios/index.html

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