
Rules with parameters in modal logic II
We analyze the computational complexity of admissibility and unifiabilit...
read it

On Axiomatization of Lewis' Conditional Logics
This paper first shows that the popular axiomatic systems proposed by Nu...
read it

Universal Proof Theory: Semianalytic Rules and Craig Interpolation
In [6], Iemhoff introduced the notion of a focused axiom and a focused r...
read it

Universal Proof Theory: Semianalytic Rules and Uniform Interpolation
In [7] and [8], Iemhoff introduced a connection between the existence of...
read it

Automating Agential Reasoning: ProofCalculi and Syntactic Decidability for STIT Logics
This work provides proofsearch algorithms and automated countermodel e...
read it

From 2sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics
We extend to natural deduction the approach of Linear Nested Sequents an...
read it

Extending Unification in EL to Disunification: The Case of Dismatching and Local Disunification
Unification in Description Logics has been introduced as a means to dete...
read it
On the proof complexity of logics of bounded branching
We investigate the proof complexity of extended Frege (EF) systems for basic transitive modal logics (K4, S4, GL, ...) augmented with the bounded branching axioms 𝐁𝐁_k. First, we study feasibility of the disjunction property and more general extension rules in EF systems for these logics: we show that the corresponding decision problems reduce to total coNP search problems (or equivalently, disjoint NP pairs, in the binary case); more precisely, the decision problem for extension rules is equivalent to a certain special case of interpolation for the classical EF system. Next, we use this characterization to prove superpolynomial (or even exponential, with stronger hypotheses) separations between EF and substitution Frege (SF) systems for all transitive logics contained in 𝐒4.2𝐆𝐫𝐳𝐁𝐁_2 or 𝐆𝐋.2𝐁𝐁_2 under some assumptions weaker than PSPACE NP. We also prove analogous results for superintuitionistic logics: we characterize the decision complexity of multiconclusion Visser's rules in EF systems for Gabbay–de Jongh logics 𝐓_k, and we show conditional separations between EF and SF for all intermediate logics contained in 𝐓_2 + 𝐊𝐂.
READ FULL TEXT
Comments
There are no comments yet.