We show that the satisfiability problem for Strategy Logic introduced by Mogavero, Murano, and Vardi is $\Pi^1_\infty$-complete, and, more strongly, computably isomorphic to true second-order arithmetic. The lower bound is established for the next-time Boolean-goal fragment of Strategy Logic. Consequently, Strategy Logic is not recursively axiomatizable, even with effectively defined $\omega$-rules.
This book explains how algorithms work, for example, by exploiting the structure of the SAT problem with an appropriate logical calculus, like resolution, but also algorithms based on “physical” principles are considered.
This work studies the satisfiability problem for FP(Ł) by presenting an algorithm and conducting an empirical evaluation over a controlled class of FP(Ł)-satisfiability instances, revealing a clear phase transition behaviour and distinctive running-time patterns.
We prove that $\mathsf{Cheq}$ is not finitely axiomatizable, resolving a longstanding open problem in intermediate and modal logics. We further prove that the undecidability of Medvedev logic implies the undecidability of $\mathsf{Cheq}$.
The goal of this paper is to refine methods in computable analysis and to employ them in the study of solutions of an optimization problem posed by Bellman. This problem asks how to find optimal (shortest) paths which do not fit into given plane figures. We show that each instance of Bellman's problem has an arbitraril...
We answer the question whether all Heyting algebras can appear as the lattice of subterminal objects of an elementary topos in the negative. Concretely, we show that the free Heyting algebra on two generators, hence also on N generators for every N greater than 2, cannot be such a Heyting algebra. The mathematical resu...
In this paper, we show that the two intuitionistic modal logics IS4 and IK4 are decidable. We provide a constructive decision procedure, that, given a formula, produces either a proof showing the formula to be valid or a finite countermodel falsifying the formula, thus also proving the finite model property for both lo...
Marianna Girlando, Roman Kuznets, Sonia Marin et al.· 1 citation
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