Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set of rules characterizing a two-argument Boolean function to the negation fragment of classical propositional logic. The properties of soundness and completeness (...) of the calculi are demonstrated. The proof of completeness is conducted by Kalmár's method. Most of the presented sequent-calculus rules have been obtained automatically, by a rule-generating algorithm implemented in Python. Correctness of the algorithm is demonstrated. This automated approach allowed us to analyse thousands of possible rules' schemes, hundreds of rules corresponding to Boolean functions, and to nd dozens of those invertible. Interestingly, the analysis revealed that the presented proof-theoretic framework provides a syntactic characteristics of such an important semantic property as functional completeness. (shrink)

The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. (...) Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction. (shrink)

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 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. (shrink)

The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5.

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. (...) In this paper it is used to consider sequent calculi with non-branching, invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions. (shrink)

The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.

Inferential erotetic logic and inquisitive semantics 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: a disjunction of all the direct answers to an evoked question is always inquisitive; a (...) formula is inquisitive if, and only if it evokes a yes–no question whose affirmative answer expresses a possibility for the formula; inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question. (shrink)

The concept of cooperative question-responses as an extension of cooperative behaviours used by interfaces for databases and information systems is proposed. A procedure to generate question-responses based on question dependency and erotetic search scenarios is presented. The procedure is implemented in Prolog.

An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic ). In this paper, a new erotetic calculus for Classical Propositional Logic ), 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. (shrink)

I consider two cognitive phenomena: inquiring and justifying, as complementary processes running in opposite directions. I explain on an example that the former process is driven by questions and the latter is a codification of the results of the first one. Traditionally, proof theory focuses on the latter process, and thus describes the former, at best, as an example of a backward proof search. I argue that this is not the best way to analyze cognitive processes driven by questions, and (...) that proof-theoretical analysis of questions can bring mutual benefits for both proof theory and erotetic logic. In the second part of my paper (sect. 6.3) I introduce the structural rules of weakening and contraction. Results concerning their admissibility are discussed. I also sketch an erotetic interpretation of the rule of weakening as reducing information noise, and that of contraction as securing information. (shrink)

This paper presents Rasiowa–Sikorski deduction systems for logics \, \, \ and \. For each of the logics two systems are developed: an R–S system that can be supplemented with admissible cut rule, and a \-version of R–S system in which the non-admissible rule of cut is the only branching rule. The systems are presented in a Smullyan-like uniform notation, extended and adjusted to the aims of this paper. Completeness is proved by the use of abstract refutability properties which are (...) dual to consistency properties used by Fitting. Also the notion of admissibility of a rule in an R–S-system is analysed. (shrink)

The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.

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

Author: Angutek Dorota Title: ON THE ROLE OF JERZY KMITA’S SEMIOTIC CONCEPTS IN DESCRIPTION OF NONVERBAL COMMUNICATION (O wykorzystaniu pojęć semiotycznych Jerzego Kmity w opisie komunikowania niewerbalnego) Source: Filo-Sofija year: 2011, vol:.12, number: 2011/1, pages: 329-346 Keywords: SEMIOTICS, SIGN, NONVERBAL COMMUNICATION, HAPTIC COMMUNICATION, CULTURE, CONVENTION Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The author discusses various approaches to nonverbal communication and tries to provide a general descriptive account of the problem in (...) order to confront it with Jerzy Kmita’s theory of culture, signs, and symbolic communication. On the base of semiotic conception of Kmita, the author sketches theoretical background which opens the possibility of conventional interpretation of nonverbal communicates and presupposes their social and cultural relativization. (shrink)

Artykuł zawiera rozważania nad zróżnicowaniem tekstów eseistycznych dotyczących problematyki polskości, wynikającym z różnorodnej roli pamięci w poszczególnych koncepcjach narodowej tożsamości. Celem szkicu jest podjęcie refleksji nad relacją, w jaką wchodzą teksty, dające się określić jako tradycjonalistyczne oraz modernizacyjne, z orientacjami esencjalistycznymi i kontruktywistycznymi. Przedmiot analizy zawartej w tekście stanowią przede wszystkim dwie publikacje: Awangardowy konserwatyzm Pawła Rojka oraz Polska: wspólnota fantazmatyczna Agaty Bielik-Robson. Eseje te pozwalają się traktować jako reprezentatywne przykłady złożonych zależności ideowych występujących w obszarze refleksji nad polskością.

The human spindle and kinetochore associated complex is required for proper mitotic progression. Extensive studies have demonstrated its important functions in both stable kinetochore-microtubule interactions and spindle checkpoint silencing. We suggest a model to explain how various Ska functions might be fulfilled by distinct pools of Ska at kinetochores. The Ndc80-loop pool of Ska is recruited by the Ndc80 loop, or together with some of its flanking sequences, and the recruitment is also dependent on Cdk1-mediated Ska3 phosphorylation. This pool seems (...) to play a more important role in silencing the spindle checkpoint than stabilizing kinetochore-microtubule interactions. In contrast, the Ndc80-N-terminus pool of Ska is recruited by the N-terminal domains of Ndc80 and appears to be more important for stabilizing kinetochore-microtubule interactions. Here, we review and discuss the evidence that supports this model and suggest further experiments to test the functioning mechanisms of the Ska complex. The human spindle and kinetochore associated complex plays essential functions in proper mitotic progression by promoting stable kinetochore-microtubule interactions and spindle checkpoint silencing. We propose that “distinct pools” of Ska—the Ndc80-loop and Ndc80-N-terminus pools—might fulfill these various functions. (shrink)

Dilemma one, Between the theoretical concepts and authorial intention -- Dilemma two, Good manners and eristic -- Dilemma three, Between strangeness and familiarity -- Dilemma four, Between scholarly research and faith.

Język nauk pedagogicznych wielokrotnie poddawany był krytyce. Jego porządkowanie należy rozpocząć od sprecyzowania pojęć: „wychowanie”, „kształcenie” i „nauczanie”, uważanych za podstawowe pojęcia pedagogiczne, a dotąd nieokreślone w sposób zyskujący aprobatę przynajmniej większości pedagogów. Większość kontrowersji i sporów dotyczy przede wszystkim treści i zakresu pojęcia „wychowanie ". Różnorodność ujęć i sposobów użycia tego terminu powoduje trudności w porozumiewaniu się, wieloznaczność i chaos w dyskusjach i rozważaniach pedagogicznych. Analiza literatury ze zwróceniem szczególnej uwagi na definicje omawianego pojęcia i codzienna praktyka pedagogiczna pozwoliły (...) na przeprowadzenie próby uświadomienia wszystkim posługującym się językiem nauk pedagogicznych trudności, z jakimi borykają się pedagodzy teoretycy w precyzowaniu swego języka. (shrink)

This article joins in and extends the contemporary debate on the right to privacy. We bring together two strands of the contemporary discourse on privacy. While we endorse the prevailing claim that norms of informational privacy protect the autonomy of individual subjects, we supplement it with an argument demonstrating that privacy is an integral element of the dynamics of all social relationships. This latter claim is developed in terms of the social role theory and substantiated by an analysis of the (...) role of privacy in intimate relationships, in professional relationships and in social interactions between strangers in public. We conclude by arguing that it is not always reasonable to assume a conflict between individual privacy on the one hand and society on the other. Legislators and participants in public debate also have to take into account the consequences of limiting privacy on social interaction and the integration of the society. (shrink)

I sitt berömda bevis för tidens overklighet påstod McTaggart att det sätt händelser tycks skifta position i tiden från framtid till nutid och till förfluten tid, innebär en motsägelse. Vad McTaggart egentligen menade har varit föremål för en livlig debatt ända sedan beviset först publicerades 1908. Beviset består av två delar. I den första argumenterar McTaggart för att ingenting kan förändras förutom genom att övergå från framtid till förfluten tid. I den andra argumenterar han för att en sådan övergång innebär (...) en motsägelse och att det därför inte kan finnas någon förändring överhuvudtaget, vilket i sin tur innebär att det heller inte finns någon tid. De flesta filosofer är i dag eniga om att McTaggart har fel, men oeniga om på vilket sätt han har fel. Olika filosofer förkastar olika delar av beviset, beroende på om de har vad som kallas en A- eller B-uppfattning av tiden. De som har en A-uppfattning förnekar att tid förstådd som övergång från framtid till förfluten tid är motsägelsefull. De som har en B-uppfattning förnekar att en övergång från framtid till förfluten tid är nödvändig för förändring, men håller med om att sådan övergång är motsägelsefull. Det är min uppfattning att denna oenighet beror på att McTaggarts argument från första början blivit missuppfattat, av både A- och B-teoretiker. Av någon anledning har det alltid betraktats som ett självständigt argument, ett som är oberoende av det ontologiska system McTaggart förespråkade. Jag föreslår ett nytt sätt att förstå hur han menade att tiden är motsägelsefull. Ett sätt som tar hans ontologiska system som utgångspunkt. (shrink)