Inconsistency-tolerant temporal reasoning with sequential (i.e., ordered or hierarchical) information is gaining increasing importance in computer science applications. A logical system for representing such reasoning is thus required for obtaining a theoretical basis for such applications. In this paper, we introduce a new logic called paraconsistent sequential linear-time temporal logic (PSLTL), which is an extension of the standard linear-time temporal logic (LTL). PSLTL can appropriately represent inconsistency-tolerant temporal reasoning with sequential information. The cut-elimination, decidability, and completeness theorems for PSLTL are proved in this paper.

The beliefs of other people about our own beliefs affect our decision making strategies (and beliefs). In epistemic game theory, player’s beliefs about other players’ beliefs are formalized, and the way how people may reason about other players (before they make their final choice in a game) is explored. In this paper, we introduce a non-self-referential paradox (called “Yablo-like Brandenburger-Keisler paradox”) in epistemic game theory which shows that modeling players’ epistemic beliefs and assumptions in a complete way is impossible. We also present an interactive temporal (belief and) assumption logic to give an appropriate formalization for this Yablo–like Brandenburger-Keisler paradox. Formalizing the new paradox turns it into a theorem in the interactive temporal assumption logic.

In this short note we show that the full generalized models of any extension of a logic can be determined from the full generalized models of the base logic in a simple way. The result is a consequence of two central theorems of the theory of full generalized models of sentential logics. As applications we investigate when the full generalized models of an extension can also be full generalized models of the base logic, and we prove that each Suszko filter of a logic determines a Suszko filter  of each of its extensions, also in a simple way.

During the Autumn School on Strongly Finite Sentential Calculi held in Międzygórze in 1977, Wójcicki conjectured that a propositional logic has a strongly adequate matrix semantics consisting of matrices with a singleton designated filter, which we call a Rasiowa semantics since it is possessed by all implicative logics of Rasiowa, if and only if it satisfies a simple technical condition that we name the Wójcicki condition. Malinowski proved the conjecture in 1978. We revisit Malinowski's Theorem in the setting of logics formalized as π-institutions.

A refutation system for Wansing's logicW(which is an expansion of Nelson's logic) is given. The refutation system provides an efficient decision procedure for W. The procedure consists in constructing for any normal form a finite syntactic tree with the property that the origin is non-valid if some end node is non-valid. The finite model property is also established.

We give a normalizing system of natural deduction for positive contraction - less relevant logic . The specific characteristic of our calculus is that it has a simple translational relationship to a particular sequent calculus for , such that normal natural deduction derivations correspond to cut-free sequent calculus derivations and vice versa. By translations from natural deduction to sequent calculus derivations, and back, together with cut-elimination, we obtain an indirect proof of the normalization.