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.
Our aim is to model the behaviour of a cognitive agent trying to solve a complex problem by dividing it into sub-problems, but failing to solve some of these sub-problems. We use the powerful framework of erotetic search scenarios (ESS) combined with Kleene's strong three-valued logic. ESS, defined on the grounds of Inferential Erotetic Logic, has appeared to be a useful logical tool for modelling cognitive goal-directed processes. Using the logical tools of ESS and the three-valued logic, we will show how an agent could solve the initial problem despite the fact that the sub-problems remain unsolved. Thus our model not only indicates missing information but also specifies the contexts in which the problem-solving process may end in success despite the lack of information. We will also show that this model of problem solving may find use in an analysis of natural language dialogues.
In this article, results of the automation of an abductive procedure are reported. This work is a continuation of our earlier research [21], where a general scheme of the procedure has been proposed. Here, a more advanced system developed to generate and evaluate abductive hypotheses is introduced. Abductive hypotheses have been generated by the implementation of the Synthetic Tableau Method. Before the evaluation, the set of hypotheses has undergone several reduction phases. To assess usefulness of abductive hypotheses in the reduced set, several criteria have been employed. The evaluation of efficiency of the hypotheses has been provided by the multi-criteria dominance relation. To comprehend the abductive procedure and the evaluation process more extensively, analyses have been conducted on a number of artificially generated abductive problems.
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