A Partial Predicate Calculus in a Two-Valued Logic

Reports on Mathematical Logic - RML, 1996

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1976

Studia Logica, 1978

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1987

Journal of Computer Science and Cybernetics, 2012

This paper refers to the representation of a set of inference formulas by their truth value table. A necessary and sufficient conditions for representing a given logical formula by a set of inference formulas are proved. An algorithm for finding a set of inference formulas by their truth value is presented. Some applications of inference formulas to Armstrong's relations are discussed. Torn tlit. Bai viet de c%p den m9t lap cong thuc logic suy din dang X-+ Y, trong d6 X va Y 111. cac tich logic cila h iru h an bien. Trong ph an thtr hai cda bai ph at bie'u va chirng minh dieu kien din va d1i de' m9t cong thtrc logic c6 the' bie'u di~n diro-idang h9i ciia cac cong tlnrc suy din. Ph an nay ciing trlnh bay v a d anh gia thuat toan xay dung h9i suy din theo bdng gia tr] cho trrro'c. Ph~n thu' ba mo ta v ai trng dung lap cac cong thuc suy din dE! khtio sat cac quan h~Amstrong trong ly th uydt CO" sOd ir li~u. Cac cong th irc logic suy dh dang X-+ Y, trong do X va Y la cac t ich logic cti a hiru h an bien

Analysis, 2000

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2021

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. For modal logics, limit behavior for models and frames may differ. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5. They also proposed zero-one laws for the corresponding classes of frames, but their zero-one law for K-frames has since been disproved. In this paper, we prove zero-one laws for provability logic with respect to both model and frame validity. Moreover, we axiomatize validity in almost all irreflexive transitive finite models and in almost all irreflexive transitive finite frames, leading to two different axiom systems. In the proofs, we use a combinatorial result by Kleitman and Rothschild about the structure of almost all finite partial orders. On the way, we also show that a previous result by Halpern and Kapron about the axiomatization of almost sure frame validity for S4 is not correct. Finally, we consider the complexity of deciding whether a given formula is almost surely valid in the relevant finite models and frames.

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1971

The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Frege's Context Principle, by taking "contributions" to sentential meanings as determined by the functionargument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types, traditionally interpreted in Henkin models. The compositionality of the resulting attribution of semantic values is discussed. Elsewhere, the same method was used for defining proof-theoretic meaning of subsentential phrases in a fragment of natural language. Doing the same for (the simpler and clearer case of) logic sheds more light on the proposal.

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1985