This paper studies the implication relations between the AGM postulates ( 7) and (+̇7) under non-classical logics, namely intuitionistic logic, paraconsistent logic, G3 and G3'. In order to do so, some theorems on the implication relations between such postulates are drawn for logics with a special set of axioms. These are later used to deduce similar results under the four logics of interest. T...

In Abstract Algebraic Logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper p...

Orthomodular logic represented by a complete orthomodular lattice has been studied as a pertinent generalization of the two-valued logic, Boolean-valued logic, and quantum logic. In this paper, we introduce orthomodular logic valued models for set theory generalizing quantum logic valued models introduced by Takeuti as well as Boolean-valued models introduced by Scott and Solovay, and prove a g...

Separation logic is used as an assertion language for Hoare-style proof systems about programs with pointers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that first-order separation logic with one record field restricted to two variables and the separating implication (no separating conjunction) is as expressive as weak second-order logic...

Many diierent fuzzy implication operators have been proposed; most of them t into one of the two classes: implication operations that are based on an explicit representation of implication A ! B in terms of &, _, and : (e.g., S-implications that are based on the formula B _ :A), and R-implications that are based on an implicit representation of implication A ! B as the weakest C for which C&B i...

We investigate an alternative language for equilibrium logic that is based on the concept of positive and negative contingency. Beyond these two concepts our language has the modal operators of necessity and impossibility and the Boolean operators of conjunction and disjunction. Neither negation nor implication are available. Our language is just as expressive as the standard language of equili...

In 1926, Ernst Mally proposed the first system of deontic logic. His system turned out to be unacceptable. How can it be repaired? We discuss several proposals to reformulate it in terms of strict implication, relevant implication and strict relevant implication.