In Béziau a logic \ was defined with the help of the modal logic \. In it, the negation operator is understood as meaning ‘it is not necessary that’. The strong soundness–completeness result for \ with respect to a version of Kripke semantics was also given there. Following the formulation of \ we can talk about \-like logics or Beziau-style logics if we consider other modal logics instead of \—such a possibility has been mentioned in [1]. The correspondence result between (...) modal logics and respective Beziau-style logics has been generalised for the case of normal logics naturally leading to soundness–completeness results [see Marcos :279–300, 2005) and Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski :185–196, 2008), :189–203, 2009) some partial results for non-normal cases are given. In the present paper we try to give similar but more general correspondence results for the non-normal-worlds case. To achieve this aim we have to enrich original Beziau’s language with an additional negation operator understood as ‘it is necessary that not’. (shrink)

In the context of modal logics one standardly considers two modal operators: possibility ) and necessity ) [see for example Chellas ]. If the classical negation is present these operators can be treated as inter-definable. However, negative modalities ) and ) are also considered in the literature [see for example Béziau ; Došen :3–14, 1984); Gödel, in: Feferman, Collected works, vol 1, Publications 1929–1936, Oxford University Press, New York, 1986, p. 300; Lewis and Langford ]. Both of them can be (...) treated as negations. In Béziau a logic \ has been defined on the basis of the modal logic \. \ is proposed as a solution of so-called Jaśkowski’s problem [see also Jaśkowski ]. The only negation considered in the language of \ is ‘it is not necessary’. It appears that logic \ and \ inter-definable. This initial correspondence result between \ and \ has been generalised for the case of normal logics, in particular soundness-completeness results were obtained [see Marcos :279–300, 2005); Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski it has been proved that there is a correspondence between \-like logics and regular extensions of the smallest deontic logic. To obtain this result both negative modalities were used. This result has been strengthened in Mruczek-Nasieniewska and Nasieniewski :261–280, 2017) since on the basis of classical positive logic it is enough to solely use \ to equivalently express both positive modalities and negation. Here we strengthen results given in Mruczek-Nasieniewska and Nasieniewski by showing correspondence for the smallest regular logic. In particular we give a syntactic formulation of a logic that corresponds to the smallest regular logic. As a result we characterise all logics that arise from regular logics. From this follows via respective translations a characterisation of a class of logics corresponding to some quasi-regular logics where \ is the smallest element. Moreover, if a given quasi-regular logic is characterised by some class of models, the same class can be used to semantically characterise the logic obtained by our translation. (shrink)

In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOL Ex defined by so called externally compatible identities of modular ortholattices.

Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p.

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics. In a logic N has been investigated in the language with negation; (...) implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation. In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21. The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+. (shrink)

In Jaśkowski’s model of discussion, discussive connectives represent certain interactions that can hold between debaters. However, it is not possible within the model for participants to use explicit modal operators. In the paper we present a modal extension of the discussive logic $\textbf{D}_{\textbf{2}}$ that formally corresponds to an extended version of Jaśkowski’s model of discussion that permits such a use. This logic is denoted by $\textbf{m}\textbf{D}_{\textbf{2}}$. We present philosophical motivations for the formulation of this logic. We also give syntactic characterizations (...) of the logic and propose a comparison with certain other modal systems. In particular, we prove that $\textbf{m}\textbf{D}_{\textbf{2}}$ is neither normal nor regular. On the basis of the axiomatization of $\textbf{D}_{\textbf{2}}$, we give an axiomatization of $\textbf{m}\textbf{D}_{\textbf{2}}$. We also give another axiomatization which is not based on the axiomatization of $\textbf{D}_{\textbf{2}}$. Furthermore, we give a natural Kripke-style semantics for $\textbf{m}\textbf{D}_{\textbf{2}}$ and prove the respective adequacy theorems. (shrink)

In [4] the lattice of all subvarieties of the variety G n Ex defined by so called externally compatible identities of Abelian groups together with the identity x n ≈ y n , for any n ∈ N and n ≥ 1 was described. In that paper classes of models of the type (2,1) where considered. It appears that diagrams of lattices of subvariaties defined by externally compatible identities satisfied in a given equational theory depend on the language of the (...) considered class of algebras. A question was asked to what extent the diagram of the lattice of subvarieties of the variety defined by externally compatible identities of a given variety will depend on changing the type of algebras. In general case, the answer to this question seems to be very complicated. In this paper we describe the variety of Abelian groups of exponent p·q, where p,q are different primes of type (2,1,0). (shrink)

Let τ : F → N be a type of a variety V . Every partition Pof the set F determines a so-called P-compatible variety. We consider thevarieties GnP defined by so-called P-compatible identities of Abelian groupswith exponent n. Besides, we study a connection between the lattice of allpartitions of the set F and the lattice of all subvarieties of the variety definedby some kind of P-compatible identities — externally compatible identitiessatisfied in the class of all Abelian groups with exponent (...) n. (shrink)

In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOLEx defined by so called externally compatible identities of modular ortholattices.

In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as $$ {\textsf {D}}_{\textsf {0}}$$ D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2 but with the help of the deontic normal logic (...) $$\textbf{D}$$ D. Although we focus on the smallest discussive logic and its correspondence to $$ {\textsf {D}}_{\textsf {2}}$$ D 2, we analyse to some extent also its formal aspects, in particular its behaviour with respect to rules that hold for classical logic. In the paper we propose a deductive system for the above recalled discussive logic. While formulating this system, we apply a method of Newton da Costa and Lech Dubikajtis—a modified version of Jerzy Kotas’s method used to axiomatize $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Basically the difference manifests in the result—in the case of da Costa and Dubikajtis, the resulting axiomatization is pure modus ponens-style. In the case of $$ {\textsf {D}}_{\textsf {0}}$$ D 0, we have to use some rules, but they are mostly needed to express some aspects of positive logic. $$ {\textsf {D}}_{\textsf {0}}$$ D 0 understood as a set of theses is contained in $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Additionally, any non-trivial discussive logic expressed by means of Jaśkowski’s model of discussion, applied to any regular modal logic of discussion, contains $$ {\textsf {D}}_{\textsf {0}}$$ D 0. (shrink)

The lattices of varieties were studied in many works (see [4], [5], [11], [24], [31]). In this paper we describe the lattice of all subvarieties of the variety $G_{Ex}^n$ defined by so called externally compatible identities of Abelian groups and the identity xⁿ ≈ yxⁿ. The notation in this paper is the same as in [2].

Perceived size is a function of viewing distance, retinal images size, and various contextual cues such as linear perspective and the size and location of neighboring objects. Recently, we demonstrated that illusion magnitudes of classic visual size illusions may be greatly enhanced or reduced by adding dynamic elements. Specifically, a dynamic version of the Ebbinghaus illusion (classically considered a “size contrast” illusion) led to a greatly enhanced illusory effect, whereas a dynamic version of the Corridor illusion (a “size constancy” illusion) (...) led to a greatly diminished illusory effect. Although these differences may arise from the different processes underlying these illusions (size contrast vs. size constancy), the dynamic variants we tested in our previous work also differed in the nature of the dynamic elements; specifically, whereas the Dynamic Ebbinghaus included a moving target and inducers that changed size and position, the Dynamic Corridor only included a moving target on a static background. Here, we explore further dynamic versions of the Ebbinghaus illusion and the Corridor and Ponzo illusions by separately manipulating three types of dynamic elements: target motion, context translation, and dynamic changes in context. Across five experiments examining 21 dynamic illusory configurations, adding target motion or a dynamically changing context separately resulted in little-to-no illusory effect. In contrast, the combination of target motion and a dynamically changing context led to a robust size illusion, consistent with an interactive effect. However, illusory effects that exceeded the matched classic, static illusory configuration were only observed for the dynamic versions of the Ebbinghaus illusion and the Revealed Ponzo illusions, in which the contextual elements changed size. We conclude that the combination of target motion and a dynamically changing context are necessary to produce dynamic size illusions, but that enhancement above and beyond static illusions may be largely specific to size contrast effects. Our results have important implications for the integration of motion signals, a ubiquitous environmental stimulus, in the perception of object size. (shrink)

This paper presents an argument for the realism about mechanisms, contents, and vehicles of mental representation at both the personal and subpersonal levels, and showcases its role in instrumental rationality and proper cognitive functioning. By demonstrating how misrepresentation is necessary for learning from mistakes and explaining certain failures of action, we argue that fallible rational agents must have mental representations with causally relevant vehicles of content. Our argument contributes to ongoing discussions in philosophy of mind and cognitive science by challenging (...) anti-realist views about the nature of mental representation, and by highlighting the importance of understanding how different agents can misrepresent in pursuit of their goals. While there are potential rebuttals to our claim, our opponents must explain how agents can be rational without having mental representations. This is because mental representation is grounded in rationality. (shrink)

SummaryInfand mortality for the period 1950—70 has been analysied in a North-Swedish isolate, a population characterized by a high incidence of schizopherenic psychoses and other neuorpsychiatric disorders. Infand mortality is higher than in Sweden generally. As many as 45·9% of the deceased infands in the population sccumbed during the first week of their life, compard to 28·1% in the general Swedish population.

In the article, composed of two parts with the titles Spektakl modernistyczny czy seans spirytystyczny? (A modernist spectacle or a spiritistic seance?) and Dlaczego Słowacki niszczy konterfekt księcia Józefa? (Why does Słowacki destroy the portrait of Prince Józef?), presents a contextual interpretation of Jan Lechoń’s poem Duch na seansie (A Ghost at a Seance). The author questions the opinion, which was widespread in literary criticism, that Lechoń together with other members of the Skamander group discredited Romantic poetry and national mythology (...) on the threshold of independence. The analysis of the poem made in the article leads to the conclusion that the poet fought stereotypes deeply rooted in public opinion, which in the eyes of the general public were also reinforced by Slowacki’s poetry. Thus, Słowacki appears at the seance to demystify a belief in the messianic, necrotic and patriotic tone of his poetry, in the bard-creator of the national Gospel, who is endowed with the power to discover absolute truths, and in the „master of the word” as well as the „creator of artistic beauty” as well as the only generally-accepted opinion. Optimistic signs of revival have dominated the symbols of suffering, the talkativeness has been replaced by silence, the word by the iconoclastic deed, the mystical heat by ironic distance. The symbols, images, references to literary texts and other signes of culture help to create a revalued portrait of Słowacki and mould a myth of gray heroism, which is a complete contrast to the myth of the „colourful uhlan”. The destruction of the portrait of Prince Józef Poniatowski and a reference to Piłsudski found in the last line of Karmazynowy poemat (The Crimson Poem) are the signs of the ideological declaration of the young poet, who referring to great Romantic tradition, discovers new and new meanings. (shrink)

Pro-social basic human values and civic involvement. The moderating role of survival vs self-expression cultural context The present study investigated a hypothesis that the pro-social values differentiated by S. Schwartz's model of basic human values - universalism and benevolence - would positively predict civic involvement. Most importantly, authors expected that the type of pro-social value that would play a dominant motivational role would depend on moderating role of the level of self-expression and benevolence - cultural value dimension developed by R. (...) Inglehart. Based on discriminant function analyses performed on the data gathered in 17 European countries through the European Social Survey conducted in 2002, authors found that universalism predicts civic involvement only in self-expression countries, whereas the role of benevolence is rather neglectable and independent of the cultural context. The results are discussed with reference to cross-cultural differences in Europe. (shrink)

In this paper, we defend a representational approach to at least some kinds of non-human psychopathology. Mentally-ill non-human minds, in particular in delusions, obsessive-compulsive disorders and similar cognitive states, are traditionally understood in purely behavioral terms. In contrast, we argue that non-human mental psychopathology should be at least sometimes not only ascribed contentful mental representation but also understood as really having these states. To defend this view, we appeal to the interactivist account of mental representation, which is a kind of (...) a constructive approach to meaning. We follow Mark Bickhard in assuming that only an organism – either human or non-human – capable of detecting its own misrepresentations is representational. However, under his autonomy-based account of biological function these minds are incapable of misrepresentations because these minds are, ex hypothesi, unable to detect error in such representations. To solve this problem, we argue that adding a historical dimension – as in Millikan’s view on mental representations – to Bickhard’s account of function makes mental misrepresentation of mentally-ill minds possible. Using Bickhard’s dynamic account of function, it is possible to explain why delusions and other mental disorders can be seen as locally functional. However, an etiological dimension can further explain why misrepresentations seem to be globally dysfunctional. Even if representational or biosemiotic hypotheses about non-human psychopathology are difficult to confirm empirically, we defend the view that they can enrich our understanding of the causes and development of such pathologies, and may constitute a new progressive research programme. (shrink)

The main aim of the present article is an outline of an intuitively adequate system of logic of the operator "being informed". Such a system should be different from the familiar systems of epistemic and doxastic logic. The principle of veracity occurring in epistemic logics does not describe adequately the information operator, since the information may be true as well as false. On the other hand, the principle of consistency of beliefs, occurring in doxastic logics, cannot be applied to information, (...) because the information can be inconsistent. Our logic of information, although it is based on Kripke's semantics, includes principles not occurring in the systems of epistemic and doxastic logics, such as the principle of incompleteness of information and the Brouwerian Axiom. We prove that this system is incomplete. We also suggest that it can be generalized to a dynamic logic in the sense of van Benthem. (shrink)