ACTA issues

Partial logic in a model-theoretic approach. Ehrenfeucht games with incomplete information

Artur WoliƄski

Acta Sci. Math. (Szeged) 77:1-2(2011), 3-26

Abstract. This is a continuation of the investigation on the partial elementary logic system introduced in [Wo97] to provide a basis for the construction of cylindric algebras describing properties of partial relations. We show the relationship between partial logic and classic elementary logic. We prove that classic logic is, in some general model-theoretic sense, interpretable in partial logic, but not vice versa. Moreover, we present --- via a theorem on the correspondence of models --- some close connections between models of partial and classic logics as well as between their theories.

AMS Subject Classification (1991): 03B60; 03C07, 03C52, 91A05, 91A80

Keyword(s): first order logic, cylindric algebras, partial relations, interpretability, two-person games, winning strategy, Boolean algebras of formulas, models, theories

Received February 22, 2010. (Registered under 13/2010.)