Semantics modulo satisfiability with applications: function representation, probabilities and game theory

Abstract In the context of propositional logics, we apply semantics modulo satisfiability—a restricted which comprehends only valuations that satisfy some specific set formulas—with aim to efficiently solve computational tasks. Three possible such applications are developed. We begin by studying possibility implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through satisfiability. theoretically investigate approaches representation concept, called satisfiability, and describe a polynomial algorithm builds representations newly introduced system. An implementation algorithm, test results ways randomly generate for testing presented. Moreover, propose an application formal verification properties neural networks means reasoning framework Logic. Then, move investigation satisfiability joint probabilistic assignments formulas Logic, is known be NP-complete problem. provide exact decision derived from combination linear algebraic methods with Also, phenomenon phase transition empirically detected. Lastly, study game theory situation observable games, games reach Nash equilibrium, however, external observer does not know what profile actions occur instance; thus, assigns subjective probabilities players actions. problem determining if these constraints coherent reducing it problems logical both Classical Propositional depending on whether pure equilibria or also mixed allowed. Such reductions rely upon complexity algorithmic discussion coherence and, also, computing maximal minimal preserves coherence. prepared Sandro Márcio da Silva Preto. E-mail : [email protected] URL: https://doi.org/10.11606/T.45.2021.tde-17062021-163257