Abstract.An erotetic calculus for a given logic constitutes a sequent-style prooftheoretical formalization of the logic grounded in Inferential Erotetic Logic (IEL). In this paper, a new erotetic calculus for Classical Propositional Logic (CPL), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic CLuN and its extensions CLuNs and mbC. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the authors knowledge, this is the first account of resolution for mbC. Last but not least, as the method is grounded in IEL, it constitutes an important tool for the so-called question-processing.

Abstract.In this paper we are applying certain strategy described by Negri and Von Plato (Bull Symb Log 4(04): [418][419][420][421][422][423][424][425][426][427][428][429][430][431][432][433][434][435] 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko's Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.

This article concerns automated generation and processing of erotetic search scenarios (ESSs). ESSs are formal constructs characterized in Inferential Erotetic Logic that enable finding possible answers to a posed question by decomposing it into auxiliary questions. The first part of this work describes a formal account on ESSs. The formal approach is then applied to automatically generate ESSs, and the resulting scenarios are evaluated according to a number of criteria. These criteria are subjected to discordance analysis that reveals their mutual relationships. Finally, knowledge concerning relationships between different values of evaluation criteria is extracted by applying Apriori—an association rules mining algorithm. The proposed approach of integration of formal erotetic logic with computational tools provides extensive insight into the former and helps with the development of efficient ESSs.

We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.