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On the pi-Calculus and Linear Logic
This paper details Abramsky's “proofs-as-processes” paradigm for interpreting classical linear logic (CLL) into a “synchronous” version of the π-calculus recently proposed by Milner (1992, 1993). Expand
Extended Curry-Howard Correspondence for a Basic Constructive Modal Logic
A Decision Procedure Revisited: Notes on Direct Logic, Linear Logic and its Implementation
Several graph-theoretic results are used to prove correspondences between systems of natural deduction, direct predicate logic, and linear logic. Expand
Subnets of proof-nets in MLL -
The paper studies the properties of the subnets of proof-nets. Very simple proofs are obtained of known results on proof-nets for MLL ? , Multiplicative Linear Logic without propositional constants.
Subnets of Proof-Nets in Multiplicative Linear Logic with MIX
- G. Bellin
- Mathematics, Computer Science
- Math. Struct. Comput. Sci.
- 1 December 1997
This paper studies the properties of the subnets of a proof-net for first-order Multiplicative Linear Logic without propositional constants extended with the rule of Mix, and gives a general method for translating Abramsky-style term assignments into proof-nets. Expand
Categorical proof theory of classical propositional calculus
- G. Bellin, M. Hyland, E. Robinson, Christian Urban
- Computer Science, Mathematics
- Theor. Comput. Sci.
- 6 November 2006
It is shown that the propositional connectives are not quite well-behaved from a traditional categorical perspective, and a more refined, but necessarily complex, analysis of how connectives may be characterised abstractly is given. Expand
Towards a Logic for Pragmatics. Assertions and Conjectures
This work gives sequent calculi of type G3i and G3im inspired by Girard's LU, with subsystems characterizing intuitionistic reasoning and some forms of classical reasoning with such operators. Expand
Pragmatic and dialogic interpretations of bi-intuitionism. Part I
It is claimed that some conceptual refinements suffice to make their “pragmatic interpretation” a bona fide representation of intuitionism, and sketches a meaning-asuse interpretation of co-intuitionism that seems to fulfil the requirements of Dummett and Prawitz’s justificationist approach. Expand