Computational isomorphisms in classical logic

Computational isomorphisms in classical logic

All standard ‘linear’ boolean equations are shown to be computationally realized within a suitable classical sequent calculus LKp. Specifically, LKp can be equipped with a cut-elimination compatible equivalence on derivations based upon reversibility properties of logical rules. So that any pair of derivations, without structural rules, of F ⇒ G and G ⇒ F , where F , G are first-order formulas ...

Computational Content of Classical Logic

Classical isomorphisms of types

The study of isomorphisms of types has been mainly carried out in an intuitionistic setting. We extend some of these works to classical logic for both call-by-name and call-by-value computations by means of polarized linear logic and game semantics. This leads to equational characterizations of these isomorphisms for all the propositional connectives.

Classical Isomorphisms for Quantum Groups

The expressions for the R̂–matrices for the quantum groups SOq2(5) and SOq(6) in terms of the R̂–matrices for Spq(2) and SLq(4) are found, and the local isomorphisms of the corresponding quantum groups are established. On leave of absence from P.N.Lebedev Physical Institute, Theoretical Department, 117924 Moscow, Leninsky prospect 53, CIS.

Computational Interpretations of Classical Linear Logic

We survey several computational interpretations of classical linear logic based on two-player one-move games. The moves of the games are higherorder functionals in the language of finite types. All interpretations discussed treat the exponential-free fragment of linear logic in a common way. They only differ in how much advantage one of the players has in the exponentials games. We discuss how ...