Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this talk, we compare three sequent calculi for bi-intuitionistic propositional logic: (1) a basic standard-style sequent calculus that restricts the premises of implication-right and exclusion...

Bi-intuitionistic logic, also known as Heyting-Brouwer logic or subtractive logic, is extended in various ways by a strong negation connective used to express commitments arising from denials. These logics have been introduced and investigated in [48]. In the present paper, an inferentialist semantics in terms of proofs, disproofs, and their duals is developed. Whereas the Brouwer-Heyting-Kolmo...

This paper investigates the semantics of the intuitionistic propositional logic (IPL) extended with subtraction, also known as the HeytingBrouwer logic or biIPL. It introduces and extends some basic concepts and theorems in the Kripke semantics of intuitionistic propositional logic to obtain new results on the exact models of fragments in the bidirectional case. The paper also includes results ...

We use second-order intuitionistic logic for two purposes in this paper: first, to formulate a large class of circumscriptive queries about logic programs; and second, to formulate a class of induction schemata that can be used to answer these queries. Then, applying the techniques of intuitionistic logic programming, we develop an interpreter (written in PROLOG) that constructs inductive proof...

It has been recently provided a characterization of Answer Sets by intuitionistic logic as follows: a literal is entailed by a program in the stable model semantics if and only if it belongs to every intuitionistically complete and consistent extension of the program formed by adding only negated literals. We show that if we replace intuitionistic logic by any si-logic the result still holds.

We give an exponential lower bound on number of proof-lines in intuitionistic propositional logic, IL, axiomatised in the usual Frege-style fashion; i.e., we give an example of IL-tautologies A1, A2, . . . s.t. every IL-proof of Ai must have a number of proof-lines exponential in terms of the size of Ai. We show that the results do not apply to the system of classical logic and we obtain an exp...

We investigate properties of monadic purely negational fragment of Intuitionistic Control Logic (ICL). This logic arises from Intuitionistic Propositional Logic (IPL) by extending language of IPL by additional new constant for falsum. Having two different falsum constants enables to define two forms of negation. We analyse implicational relations between negational monadic formulae and present ...

We show that the model checking problem for intuitionistic propositional logic with one variable is complete for logspace-uniform AC. As basic tool we use the connection between intuitionistic logic and Heyting algebra, and investigate its complexity theoretical aspects. For superintuitionistic logics with one variable, we obtain NC-completeness for the model checking problem.

We present a Prolog program that implements a sound and complete theorem prover for rst-order intuitionistic logic. It is based on free-variable semantic tableaux extended by an additional string uniica-tion to ensure the particular restrictions in intuitionistic logic. Due to the modular treatment of the diierent logical connectives the implementation can easily be adapted to deal with other n...