An embedding of the implicational propositional intuitionistic logic (iil) into the nonmodal fragment of intuitionistic linear logic (imall) is given. The embedding preserves cut-free proofs in a proof system that is a variant of iil. The embedding is eecient and provides an alternative proof of the pspace-hardness of imall. It exploits several proof-theoretic properties of intuitionistic impli...

During years of research, there have been defined 153 intuitionistic fuzzy implications. In the paper, it is checked which of these implications satisfy which axioms of the intuitionistic logic, whether as (classical) tautologies or as intuitionistic fuzzy tautologies. Some open problems, related to the operations of intuitionistic fuzzy propositional calculus, are formulated.

In this paper, we propose an intuitionistic semantics for negation-as-failure in logic programs. The basic idea is to work with the completion of the program, not in classical logic, but in intuitionistic (or, more precisely, minimal) logic. Moreover, we consider two forms of completion: (1) rst-order predicate completion, as de ned by Clark, which is related to SLDNF resolution; and (2) second...

In this paper, we propose an intuitionistic semantics for negation-as-failure in logic programs. The basic idea is to work with the completion of the program, not in classical logic, but in intuitionistic (or, more precisely, minimal) logic. Moreover, we consider two forms of completion: (1) first-order predicate completion, as defined by Clark, which is related to SLDNF resolution; and (2) sec...

We present a modal extension of classical propositional logic in which intuitionistic propositional logic is mirrored by means of the modal operator. In this sense, the modal extension combines classical and intuitionistic propositional logic avoiding the collapsing problem. Adopting ideas from a recent paper (S. Lewitzka, A denotational semantics for a Lewis-style modal system close to S1, 201...

This paper shows that classical logic is inappropriate for hypothetical reasoning and develops an alternative logic for this purpose. The paper focuses on a form of hypothetical reasoning which appears computationally tractable. Specifically, Horn-clause logic is augmented with rules, called embedded implications, which can hypothetically add atomic formulas to a rulebase. By introducing the no...