Classical logic as limit completion

Authors:
Stefano Berardi
Affiliations:
Computer Science Department, Università di Torino, Corso Svizzera 185, 10149 Torino, Italy http://www.di.unito.it/~stefano
Venue:
Mathematical Structures in Computer Science
Year:
2005

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Abstract

We define a constructive model for ${\Delta^0_2}$-maps, that is, maps recursively definable from a map deciding the halting problem. Our model refines an existing constructive interpretation for classical reasoning over one-quantifier formulas: it is compositional (Modus Ponens is interpreted as an application) and semantical (rather than translating classical proofs into intuitionistic ones, we define a mathematical structure intuitionistically validating excluded middle for one-quantifier formulas).