Several Gentzen-style syntactic type calculi with product are considered. They form a hierarchy in such a way that one calculus results from another by imposing a new condition upon the sequent-forming operation. It turns out that, at some steps of this process, two different functors collapse to a single one. For the remaining stages of the hierarchy, analogues of Wajsbergs's theorem on non-mutual-definability are proved.

In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen [3] proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz [1]. For the reasons which will be discussed in the last section, (...) Cohen's proof seems to be at least incomplete. This paper yields a direct proof of the equivalence ofFCGs andSPGs. (shrink)

In Zielonka (1981a, 1989), I found an axiomatics for the product-free calculus L of Lambek whose only rule is the cut rule. Following Buszkowski (1987), we shall call such an axiomatics linear. It was proved that there is no finite axiomatics of that kind. In Lambek's original version of the calculus (cf. Lambek, 1958), sequent antecedents are non empty. By dropping this restriction, we obtain the variant L0 of L. This modification, introduced in the early 1980s (see, e.g., Buszkowski, (...) 1985; Zielonka, 1981b), did not gain much popularity initially; a more common use of L0 has only occurred within the last few years (cf. Roorda, 1991: 29). In Zielonka (1988), I established analogous results for the restriction of L0 to sequents without left (or, equivalently, right) division. Here, I present a similar (cut-rule) axiomatics for the whole of L0.This paper is an extended, corrected, and completed version of Zielonka (1997). Unlike in Zielonka (1997), the notion of rank of an axiom is introduced which, although inessential for the results given below, may be useful for the expected non-finite-axiomatizability proof.The paper follows the same way of subject exposition as Zielonka (2000) but it is technically much less complicated. I restrict myself to giving bare results; all the ideological background is exactly the same as in case of the non-associative calculusNL0 and those who are interested in it are requested to consult the introductory section of Zielonka (2000). (shrink)

In [4], I proved that the product-free fragment L of Lambek's syntactic calculus (cf. Lambek [2]) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut-rule. The proof (which is rather complicated and roundabout) was subsequently adapted by Kandulski [1] to the non-associative variant NL of L (cf. Lambek [3]). It turns out, however, that there exists an extremely simple method of non-finite-axiomatizability proofs which works uniformly for different subsystems of L (in particular, for NL). We (...) present it below to the use of those who refer to the results of [1] and [4]. (shrink)

An axiomatics of the product-free syntactic calculus L ofLambek has been presented whose only rule is the cut rule. It was alsoproved that there is no finite axiomatics of that kind. The proofs weresubsequently simplified. Analogous results for the nonassociativevariant NL of L were obtained by Kandulski. InLambek's original version of the calculus, sequent antecedents arerequired to be nonempty. By removing this restriction, we obtain theextensions L 0 and NL 0 ofL and NL, respectively. Later, the finiteaxiomatization problem for L (...) 0 andNL 0 was partially solved, viz., for formulas withoutleft (or, equivalently, right) division and an (infinite) cut-ruleaxiomatics for the whole of L 0 has been given. Thepresent paper yields an analogous axiomatics forNL 0. Like in the author's previous work, the notionof rank of an axiom is introduced which, although inessentialfor the results given below, may be useful for the expectednonfinite-axiomatizability proof. (shrink)

The paper continues a series of results on cut-rule axiomatizability of the Lambek calculus. It provides a complete solution of a problem which was solved partially in one of the author''s earlier papers. It is proved that the product-free Lambek Calculus with the empty string (L 0) is not finitely axiomatizable if the only rule of inference admitted is Lambek''s cut rule. The proof makes use of the (infinitely) cut-rule axiomatized calculus C designed by the author exactly for this purpose.

In Zielonka (1981a, 1989), I found an axiomatics for the product-free calculus L of Lambek whose only rule is the cut rule. Following Buszkowski (1987), we shall call such an axiomatics linear. It was proved that there is no finite axiomatics of that kind. In Lambek's original version of the calculus (cf. Lambek, 1958), sequent antecedents are non empty. By dropping this restriction, we obtain the variant L 0 of L. This modification, introduced in the early 1980s (see, e.g., (...) Buszkowski, 1985; Zielonka, 1981b), did not gain much popularity initially; a more common use of L 0 has only occurred within the last few years (cf. Roorda, 1991: 29). In Zielonka (1988), I established analogous results for the restriction of L 0 to sequents without left (or, equivalently, right) division. Here, I present a similar (cut-rule) axiomatics for the whole of L 0. This paper is an extended, corrected, and completed version of Zielonka (1997). Unlike in Zielonka (1997), the notion of rank of an axiom is introduced which, although inessential for the results given below, may be useful for the expected non-finite-axiomatizability proof. (shrink)

Joel M. Cohen , pp. 475- 484) claims that Lambek’s categorial grammars are equivalent in a certain natural sense to those of Bar-Hillel, Gaifman, and Shamir. Unfortunately, it turns out that Cohen’s proof is based on a false lemma. Thus the equivalence of both kinds of grammars is still an open problem although there is much evidence in its favor. This paper yields a counterexample to Cohen’s lemma.

Axiomatics which do not employ rules of inference other than the cut rule are given for commutative product-free Lambek calculus in two variants: with and without the empty string. Unlike the former variant, the latter one turns out not to be finitely axiomatizable in that way.

In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars dened by Chomsky are equivalent in a cer- tain sense to Bar-Hillel's bidirectional categorial grammars . On the other hand, Cohen [3] proves the equivalence of the latter ones to what he calls free categorial grammars . They are closely related to Lambek's syntactic calculus which is, in turn, based on the idea due to Ajdukiewicz [1]. For some reasons, Cohen's proof seems to be at least in- (...) complete. Here, I give a short outline of the direct proof of the equivalence between SF G's and F CG's. (shrink)

The calculus DNL results from the non-associative Lambek calculus NL by splitting the product functor into the right (⊲) and left (⊳) product interacting respectively with the right (/) and left () residuation. Unlike NL, sequent antecedents in the Gentzen-style axiomatics of DNL are not phrase structures (i.e., bracketed strings) but functor-argument structures. DNL − is a weaker variant of DNL restricted to fa-structures of order ≤ 1. When axiomatized by means of introduction/elimination rules for / and , it shows (...) a perfect analogy to NL which DNL lacks. (shrink)

Celem artykułu jest przedstawienie twórczości Pawła Jaszczuka, który dzięki swoim dokonaniom stał się reprezentatywny, zarówno dla literatury kryminalnej, jak i dla środowiska Warmii i Mazur. Od wielu lat pisze powieści kryminalne, przyczyniając się do rozwoju odmian gatunku, a jednocześnie korzystając z tej formy, porusza ważne współcześnie tematy. W jego utworach widać także przebieg pewnego procesu: rozpoczynając od narracji historycznej, w której ważne miejsce pełniła przeszłość, coraz częściej zabiera głos w sprawie teraźniejszości i jej wyznaczników: dominacji polityki w życiu, rozprzestrzeniania się (...) kultury masowej, rozpadu rodziny czy wszechobecnego ageizmu. Przedstawienie jego powieści kryminalnych ma wykazać, że w jego metodzie twórczej z jednej strony widoczna jest tendencja do eksponowania tematów związanych z przeszłością, a z drugiej strony mechanizm łączenia narracji historycznej z wątkami popkulturowymi. (shrink)

Traditional martial arts continue to be interesting and inspiring to many people around the globe. Some of their contemporary adaptations attract enthusiasts for whom they are especially important. In this article, the author bases his observations on his own long-term participation. The analysis takes into account the influence of the perspectives of Jigoro Kano and several other creators of modern varieties of Japanese budo. It can be concluded that regular, even daily, practice—cultivating martial arts and internalizing its values—co-creates the lifestyle (...) of instructors and advanced students. (shrink)

Polskie przepisy prawne formułujące warunki dopuszczalności eksperymentu medycznego, a więc ipso facto wyznaczające jego granice, można różnorako interpretować, zwłaszcza w tym zakresie, w jakim określają wymagany dla przeprowadzenia eksperymentu bilans związanych z nim możliwych korzyści i szkód. W artykułach prawniczych komentujących te przepisy w zasadzie jednak brak prób systematycznego i (na tyle, na ile pozwala na to sam przedmiot analizy) ścisłego wyróżnienia tych interpretacji w języku tzw. teorii racjonalnego wyboru (rational choice theory), teorii szczególnie przydatnej w tym kontekście z uwagi (...) na jej rozbudowany aparat pojęciowy pozwalający badać różnorakie konfiguracje relacji między costs i benefits. Artykuł próbuje wypełnić tę lukę: wyróżnione w nim zostały różne interpretacje przepisów prawnych określających warunki dopuszczalności eksperymentu medycznego; interpretacje te zostały również poddane ocenie. (shrink)

Kazimierz Twardowski attributed high cognitive value to introspection because he believed it plays a fundamental role in psychology, the primary philosophical discipline. He believed that basing philosophy on inner experience would allow it to obtain universal and justified results. Internal experience consists of perceiving one’s own mental facts; it is non-sensual and selfevident. Twardowski referred to introspection in his investigations in various ways, which is presented in the article.

The Limits of Cognition and the Shape of Being Based on the Thought of Karl Jaspers The article points out the elements of Karl Jaspers’ epistemological conception that cross out the possibility of a comprehensive account of being. The key issue here is the limits of cognition, which take the form of object cognition. The theme of limits points to the inadequacies of human thinking in the context of quantifiable and absolutist representations of reality. The impossibility of adequately grasping the (...) totality of reality will be illustrated here by means of the criticism Jaspers levelled at absolutising metaphysics. In connection with the description of the structure of cognition proposed by Jaspers, the article points out the conceptual proximity of the issue of worldview and metaphysics in the light of the thought of the cited author. (shrink)

Expression of physical motion (e.g., man runs by) shows systematic variability not only between language types (i.e., inter-typological) but also within a language type (i.e., intra-typological). In this study, we asked whether the patterns of variability extend to metaphorical motion events (e.g., time runs by). Our analysis of randomly selected 450 physical motion (150/language) and 450 metaphorical motion (150/language) event descriptions from written texts originally produced by German, Polish, and Spanish authors showed strong inter-typological differences in the expression of both (...) event types. German and Polish speakers differed from Spanish speakers in how they packaged manner and path components of a motion event; they also differed in how extensively they expressed each component in their lexicalization of motion. The strong inter-typological differences were accompanied by more modest intra-typological variability: Polish and German writers differed in their packaging and lexicalization of manner and path components of metaphorical—but not physical—motion events. Our results provide evidence for robust inter-typological differences evident in the expression of both physical and metaphorical motion, along with less robust intra-typological differences, largely evident in the expression of metaphorical motion. Our study thus highlights event type as an important factor in determining crosslinguistic variation in motion expression. (shrink)

This is an account of the Uprising fights of a young machinegunner of the “Baszta” Unit from the “W” hour to the honorable surrender at the end of September.

We propose a non-standard interpretation of Alternating-time Temporal Logic with imperfect information, for which no commonly accepted semantics has been proposed yet. Rather than changing the semantic structures, we generalize the usual interpretation of formulae in single states to sets of states. We also propose a new epistemic operator for ?practical? or ?constructive? knowledge, and we show that the new logic (which we call Constructive Strategic Logic) is strictly more expressive than most existing solutions, while it retains the same model (...) checking complexity. Finally, we study properties of constructive knowledge and other operators in this non-standard semantics. (shrink)

SummaryThe Bohr‐Einstein debate on the interpretation of quantum mechanics may be viewed as a discussion on the epistemological status of knowledge gained by physics. It is shown that in fact the advent of quantum theory has led, in a new context, to an old philosophical controversy between epistemological realism and phenomenalism . An inquiry into this controversy, taking into account the contemporary understanding of quantum mechanics based on the axiomatic study of its foundations, leads to the conclusion that contrary to (...) widespread opinion, it is perfectly possible to formulate quantum mechanics in an entirely realistic manner according to the postulate of Einstein. We demonstrate that Bohr's episteme‐logy, in which the role of experimental arrangements in the physical description is taken as a starting point, does not necessarily imply phenomenlism, but may be justifiably considered as a complementary standpoint to the realistic epistemology of Einstein, which is based on the notion of a mental construction which pictures reality. (shrink)

Using randomly generated sequences of binary events we asked participants to make predictions about the next event. It turned out that while predicting uncertain events, people do not behave unsystematically. Our research identifies four types of relatively consistent strategies for predicting uncertain binary events: a strategy immune to short-run sequential dependencies consisting of the persistent prediction of long-run majority events, hereafter called the long-run momentum strategy ; a strategy immune to short-run sequential dependencies consisting of the persistent prediction of long-run (...) minority events, called the long-run contrarian strategy ; a strategy sensitive to short-run sequential dependencies consisting of the prediction of short-run majority events, called the short-run momentum strategy ; and a strategy sensitive to short-run sequential dependencies consisting of the prediction of short-run minority events, called the short-run contrarian strategy . When the character of events remains unknown, the most common strategy is the short-run momentum strategy. With the increase of a perceived randomness of the situation, people tend more often to use the short-run contrarian strategy. People differ in their general beliefs about the continuation or reversal of a trend in various natural and social processes. Trend believers, when facing sequences of binary events commonly perceived as random, tend to use momentum strategies, whereas those who believe in the trend's reversal tend to use contrarian strategies. (shrink)

This is a completely revised and updated second edition of Rights Before Courts (2005, paper edition 2008). This book carefully examines the most recent wave of the emergence and case law of activist constitutional courts: those that were set up after the fall of communism in Central and Eastern Europe. In contrast to most other analysts and scholars, the study does not take for granted that they are a "force for good" but rather subjects them to critical scrutiny against a (...) background of wide-ranging comparative and theoretical analysis of constitutional judicial review in the modern world. The new edition takes in new case law and constitutional developments in the decade since the first edition, including considering the recent disturbing disempowerment of the Hungarian Constitutional Court (which previously was probably the most powerful constitutional court in the world) resulting from the fundamental constitutional changes brought about by the Fidesz government. (shrink)

In [5] we study Nonassociative Lambek Calculus augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus. Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.