
A categorical reduction system for linear logic
We build calculus on the categorical model of linear logic. It enables u...
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Pomset logic: a logical and grammatical alternative to the Lambek calculus
Thirty years ago, I introduced a non commutative variant of classical li...
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Game Comonads Generalised Quantifiers
Game comonads, introduced by Abramsky, Dawar and Wang and developed by A...
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Constructive Game Logic
Game Logic is an excellent setting to study proofsaboutprograms via th...
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Concurrent Separation Logic Meets Template Games
An old dream of concurrency theory and programming language semantics ha...
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Computability logic: Giving Caesar what belongs to Caesar
The present article is a brief informal survey of computability logic ...
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Datalog: Bag Semantics via Set Semantics
Duplicates in data management are common and problematic. In this work, ...
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On the Unity of Logic: a Sequential, Unpolarized Approach
The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that the linear refinement of classical logic (CL) coincides with (classical) linear logic (LL), and its intuitionistic restriction with the linear refinement of intuitionistic logic (IL) into intuitionistic LL (ILL). However, LL is, in contradiction to the name, cannot be the linear refinement of CL at least from the gamesemantic point of view due to its concurrency and polarization. In fact, existing game semantics of LL employs concurrency, which is rather exotic to game semantics of ILL, IL or CL. Also, linear negation in LL is never true in (game semantics of) ILL, IL or CL. In search for the truly linear refinement of CL, we carve out (a sequent calculus of) linear logic negative (LL^) from (the twosided sequent calculus of) LL, and introducing a new distribution axiom ! ? A ? ! A (for a translation of sequents ΔΓ for CL into the sequents ! Δ ? Γ for LL^). We then give a categorical semantics of LL^, for which we introduce why not monad ?, dual to the wellknown of course comonad !, giving a categorical translation Δ→Γ = ? (ΔΓ) ! Δ ? Γ of CL into LL^, which is the Kleisli extension of the standard translation Δ→Γ = ! ΔΓ of IL into ILL. Moreover, we instantiate the categorical semantics by fully complete (sequential, unpolarized) game semantics of LL^ (without atoms), for which we introduce linearity of strategies.
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