Probably half true: probabilistic satisfiability over Łukasiewicz infinitely-valued logic. We study probabilistic-logic reasoning in a context that allows for “partial truths”, focusing on computational and algorithmic properties of non-classical Łukasiewicz infinitely-valued probabilistic logic. In particular, we study the satisfiability of joint probabilistic assignments, which we call LIPSAT. Although the search space is initially infinite, we provide linear algebraic methods that guarantee polynomial size witnesses, placing LIPSAT complexity in the NP-complete class. An exact satisfiability decision algorithm is presented which employs, as a subroutine, the decision problem for Łukasiewicz infinitely-valued (non probabilistic) logic, that is also an NP-complete problem. We develop implementations of the algorithms described and discuss the empirical presence of a phase transition behavior for those implementations.
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References in zbMATH (referenced in 6 articles , 1 standard article )
Showing results 1 to 6 of 6.
- Mundici, Daniele: Rota’s Fubini lectures: the first problem (2021)
- Mundici, Daniele: Deciding Koopman’s qualitative probability (2021)
- Finger, Marcelo; Preto, Sandro: Probably partially true: satisfiability for Łukasiewicz infinitely-valued probabilistic logic and related topics (2020)
- Preto, Sandro; Finger, Marcelo: An efficient algorithm for representing piecewise linear functions into logic (2020)
- Finger, Marcelo: Quantitative logic reasoning (2018)
- Finger, Marcelo; Preto, Sandro: Probably half true: probabilistic satisfiability over Łukasiewicz infinitely-valued logic (2018)