Multi Lingual Sequent Calculus and Coherent Spaces

We study a Gentzen style sequent calculus where the formulas on the left and right of the turnstile need not necessarily come from the same logical system. Such a sequent can be seen as a consequence between diierent domains of reasoning. We discuss the ingredients needed to set up the logic generalized in this fashion. The usual cut rule does not make sense for sequents which connect diierent ...

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Multi Lingual Sequent

We study a Gentzen style sequent calculus where the formulas on the left and right of the turnstile need not necessarily come from the same logical system. Such a sequent can be seen as a consequence between diierent domains of reasoning. We discuss the ingredients needed to set up the logic generalized in this fashion. The usual cut rule does not make sense for sequents which connect diierent ...

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Sequent Calculus 3.1 Cut-free Sequent Calculus

In the previous chapter we developed linear logic in the form of natural deduction , which is appropriate for many applications of linear logic. It is also highly economical, in that we only needed one basic judgment (A true) and two judgment forms (linear and unrestricted hypothetical judgments) to explain the meaning of all connectives we have encountered so far. However, it is not immediatel...

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Sequent Calculus 3.1 Cut-free Sequent Calculus

In the previous chapter we developed linear logic in the form of natural deduction , which is appropriate for many applications of linear logic. It is also highly economical, in that we only needed one basic judgment (A true) and two judgment forms (linear and unrestricted hypothetical judgments) to explain the meaning of all connectives we have encountered so far. However, it is not well-suite...

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Parametric Mixed Sequent Calculus

In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.

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Multi Lingual Sequent Calculus and Coherent Spaces

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