# (2(10)/2016) Andrzej Wiśniewski, Deduction and Reduction Theorems for Inferential Erotetic Logic. Research report

Abstract: Inferential Erotetic Logic (IEL) is a logic of questions that focusses its attention on inferential aspects of questioning. Validity of inferences in which questions play the role of conclusions is defined in IEL, depending on type of inference considered, in terms of question evocation or erotetic implication. The former is a binary relation between a question and a set of declaratives, while the latter is a ternary relation between a question, a set of declaratives, and a question. In this paper, deduction theorems for question evocation and erotetic implication are proven. It is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set. It is also shown how erotetic implication based on a finite non-empty set of declaratives can be reduced to a binary relation between questions only. Some consequences of the presented results are discussed.

# (1(9)/2016) Andrzej Wiśniewski, Strong Entailments and Minimally Inconsistent sets. Research Report

Abstract: Some non-monotonic relations of single- and multiple-conclusion entailment based on minimally inconsistent sets are defined and analyzed. A proof-theoretic account of minimally inconsistent sets is provided. Applications concerning minimal disjunctions, contraction, and argument analysis are presented.

# (3(8)/2015) Andrzej Wiśniewski, An Axiomatic Account of Question Evocation. Part I: The Propositional Case. Research Report

Abstract: A sequent-style axiomatic system for question evocation in Classical

Propositional Logic is proposed. Soundness and completeness of the system are proven.

# (2(7)/2015) Mariusz Urbański, Alexander Bolotov, Vasilyi Shangin, Oleg Grigoriev, Socratic Proofs for Propositional Linear-Time Logic. Research Report

Abstract: In this paper we present a calculus of Socratic proofs for Propositional Linear-Time Logic.

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# (1(6)/2015) Szymon Chlebowski, Dorota Leszczyńska-Jasion, Erotetic Calculi, Duality and Proof-Search. Research Report

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# (3(5)/2014) Mariusz Urbanski, Permittance Erotetic Implication. Research Report

Introduction: This research report presents some results on question raising as modelled in the logic of permittance (Wisniewski [2013]). The rst section of the report oers some theorems concerning basic semantic notions of this logic: permittance, transmission of permittance, logical entailment, and epistemic modality (of knowledge in a state”). In the second section some paradoxes of irrelevant permittance evocation of questions are given. The third section presents examples of two versions of permittance erotetic implication, and some theorems on their relationships. The report is not self-contained: for all the notions and symbols used here the reader should refer to Wisniewski [2013].

# (2(4)/2014) Mariusz Urbanski, Katarzyna Paluszkiewicz, and Joanna Urbanska, Deductive Reasoning and Learning: a Cross-Curricular Study. Research Report

Abstract: We report a research on correlations between level of fluid intelligence and fluencies in two kinds of deductions, simple (syllogistic reasoning) and dificult ones (erotetic reasoning), and on the impact of learning logic on fluencies in deductive reasoning. We observed that although participants of higher ability (with respect to fluid intelligence) performed better than participants of lower ability in both kinds of deductive tasks, those who undergone extensive training in formal logic obtained significantly higher results than the rest of this group in tasks involving dificult deductions. We conclude on this basis that fluency in dificult deductions, while related to fluid intelligence, is related also to subjects’ educational experience and that this does not hold in case of simple deductions.

Keywords: fluid intelligence, deductive reasoning, erotetic reasoning,

learning logic.

# (1(3)/2014) Mariusz Urbański, Identifying minimal truth conditions and minimal synthetic tableaux for CPC formulas. Research Report

Abstract: In this paper I shall give a method of identifying minimal truth conditions and minimal synthetic tableaux for a given formula A of Classical Propositional Calculus, via reduction of clausal Disjunctive Normal Form of A.

# (2(2)/2013) Andrzej Wiśniewski, Dorota Leszczyńska-Jasion, Inferential Erotetic Logic meets Inquisitive Semantics. Research Report

Abstract: Inferential Erotetic Logic (IEL) and Inquisitive Semantics (INQ) give accounts of questions and model various aspects of questioning. In this paper we concentrate upon connections between inquisitiveness, being the core concept of INQ, and question raising, characterized in IEL by means of the concepts of question evocation and erotetic implication. We consider the basic system InqB of INQ, remain at the propositional level and show, inter alia, that: (1) a disjunction of all the direct answers to an evoked question is always inquisitive; (2) a formula is inquisitive if, and only if it evokes a yes-no question whose affirmative answer expresses a possibility for the formula; (3) inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and (4) each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question.

Keywords: Logic of questions, Inferential Erotetic Logic, Inquisitive Semantics

# (1(1)/2013) Dorota Leszczyńska-Jasion, Erotetic Search Scenarios as families of sequences and Erotetic Search Scenarios as trees: two different, yet equal accounts

Abstract: Our aim is to show that two different accounts of erotetic search scenarios — namely, e-scenarios defined as families of interconnected sequences and e-scenarios defined as labelled trees — may be considered as equal.

Keywords: erotetic search scenarios