New papers in the latest issue of JALs

The Journal of Applied Logic’s latest issue features two new papers by some of our group members. You can easily access them at this link.

M. D’Agostino, C. Larese and S. ModgilTowards Depth-bounded Natural Deduction for Classical First-order Logic

Abstract: In this paper we lay the foundations of a new proof-theory for classical first-order logic that allows for a natural characterization of a notion of inferential depth. The approach we propose here aims towards extending the proof-theoretical framework presented in [6] by combining it with some ideas inspired by Hintikka’s work [18]. Unlike standard natural deduction, in this framework the inference rules that fix the meaning of the logical operators are symmetrical with respect to assent and dissent and do not involve the discharge of formulas. The only discharge rule is a classical dilemma rule whose nested applications provide a sensible measure of inferential depth. The result is a hierarchy of decidable depth-bounded approximations of classical first-order logic that expands the hierarchy of tractable approximations of Boolean logic investigated in [11, 10, 7].

M. Fait and G. PrimieroHTLC: Hyperintensional Typed Lambda Calculus

Abstract: In this paper we introduce the logic HTLC, for Hyperintensional Typed Lambda Calculus. The system extends the typed λ-calculus with hyperintensions and related rules. The polymorphic nature of the system allows to reason with expressions for extensional, intensional and hyperintentsional entities. We inspect meta-theoretical properties and show that HTLC is complete in Henkin’s sense under a weakening of the cardinality constraint for the domain of hyperintensions.

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