Game semantics for first-order logic

Olivier Laurent (1)

1 PPS - Preuves, Programmes et Systèmes

We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results. We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of first-order classical logic. We present some relations with Krivine's classical realizability and applications to type isomorphisms.

Mots clés: game semantics; first-order logic; classical logic; intuitionistic logic; lambda-calculus; lambda-mu-calculus; full completeness; type isomorphisms; realizability; control category

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]

Olivier Laurent. Game semantics for first-order logic. Logical Methods in Computer Science, 2010, 6 (4), pp.3. ⟨10.2168/LMCS-6(4:3)2010⟩. ⟨hal-00528528⟩