DoSen, K. Nonmodal classical linear predicate logic is a fragment of intuitionistic linear logic, Theoretical Computer Science 102 (1992) 207-214. It is shown that nonmodal classical linear first-order predicate logic based on multiplicative conjunction, additive disjunction, negation, the propositional constants and the existential quantifier is included in intuitionistic linear first-order pr...

In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish some relations between mixed logic and minimal, intuitionistic and classical logics. We present at the end a sequent calculus version for this logic.

This paper introduces a logic ILED derived from standard intuitionistic predicate logic by adding two operators Dφ for “Definitely φ” and ~φ for “Experience rejects φ”. A further negation ¬φ =def (φ→⊥) ∨ ~φ , which we call real negation, is introduced. Real negation is like intuitionistic negation when there are no D-operators but deviates when there are. We see that Dφ ↔ φ is valid but ¬Dφ → ¬...

Models of intuitionistic linear logic also provide models of Moggi's computational metalanguage. We use the adjoint presentation of these models and the associated adjoint calculus to show that three translations , due mainly to Moggi, of the lambda calculus into the computational metalanguage (direct, call-by-name and call-by-value) correspond exactly to three translations , due mainly to Gira...