The paper describes a system for dealing with nestings of belief in terms of the mechanism of computational environment. A method is offered for computing the beliefs of A about B (and so on) in terms of the systems existing knowledge structures about A and B separately. A proposal for belief percolation is put forward: percolation being a side effect of the process of the computation of nested beliefs, but one which could explain the acquisition of unsupported beliefs. It is (...) argued that the mechanism proposed is compatible with a general least effort hypothesis concerning human mental functioning. (shrink)

The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued ukasiewicz logic C ) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).

In the late forties, Stanisław Jaśkowski published two papers onthe discursive sentential calculus, D2. He provided a definition of it by an interpretation in the language of S5 of Lewis. The knownaxiomatization of D2 with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however,that one of the axioms they used is not a thesis of the real Jaśkowski’s calculus. In fact, they built a new system, D∗2 for short, that differs from (...) D2 inmany respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness andcompleteness theorems. Additionally, we present labelled tableaux for D∗2.1. (shrink)

The Absolute is a basic and fundamental issue for philosophy as such. I present different concepts of the Absolute (substantialism, energetism, escapism, methodologism). We can say that contemporary European philosophy “orphaned” the neo-Platonic tradition. Thereafter Russian philosophy developed in an intensive and turbulent as well as relatively uniform fashion, in view of the well-established Neo-Platonist context. This makes Russian philosophy not only part of a lasting universally acknowledged tradition; not only has Russian philosophy continued to develop currents of thought abandoned (...) by modern European philosophiers, but it is also heir to a philosophical tradition of particular quality and value in the universal history of thought. (shrink)

The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.

This study investigates performance of portfolios composed of British socially responsible investments (SRI) stocks. Using the ‘Global-100 Most Sustainable Corporations in the World’ list (known also as ‘Global-100’) to select the SRI companies, we found that, in the period 2000–2010, the returns of the SRI portfolios were on average higher compared with the corresponding returns of the market indexes. The annual average difference in returns of the SRI portfolios (with dividends) was 5.26 % and 5.69 % relative to the FTSE100 (...) and FTSE4GOOD indexes (the total return versions), respectively, but the differences in returns in the whole period, in individual years and in other sub-periods were in most cases not statistically significant. Positive performance of SRI stocks in the whole sample is, however, evidenced by risk-adjusted measures such as the modified Sharpe ratio (MSR) and certainty equivalent (CEQ) returns, as well as by incorporating various levels of transaction costs. Furthermore, a simple trading strategy relying on selection of SRI stocks from the Global-100 list would beat the market indexes in the whole period 2000–2010, even after inclusion of various levels of transaction costs. We also estimated the Fama–French and Carhart multi-factor models and found that the returns of the SRI portfolios cannot be consistently explained by conventional factors other than the market factor. (shrink)

W tym artykule zaproponuję konstrukcję trójwartościowej logiki przekonań, którą nazywam: LSB3_1. Podam również i udowodnię kompletność LSB3_1 w odniesieniu do danej semantyki. LSB3_1 opiera się na preformalnych założeniach i intuicjach, które przedstawiono w sekcji 1. Sekcja 2 zawiera składnię i podział instrukcji LSB3_1 na wewnętrzne i zewnętrzne. Rozdział 3 przedstawia semantykę LSB3_1, a także szereg tautologii i formuł nietautologicznych w LSB3_1 wraz z ich intuicyjną interpretacją. System aksjomatyczny dla LSB3_1 i jego porównanie z silną logiką Kleene'a są przedstawione w sekcji (...) 4. Twierdzenie o kompletności dla LSB3_1 jest przedstawione w rozdziale 5. Zdefiniuję termin koniunkcyjna forma normalna i przedstawię lematy, które prowadzą do udowodnienia redukcji języka LSB3_1 wzory przed udowodnieniem twierdzenia o zupełności. (shrink)

One can speak about mathematics too simplistically. On the one hand, school programs are such examples. On the other hand, the function of mathematics in elementary physics very much indicates the profound philosophical significance of mathematics: the author claims that mathematical language is a kind of command language, i.e. it is not just a description, but a control which has a specific power to manage the reality. This language has its proper hierarchy and structures which humans only are just starting (...) to understand and to use in basic ways, not without errors. Therefore some ethics regarding human mathematical thinking are needed: the affirmation of life. (shrink)

The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...) of matrices containing K and closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images. (shrink)

In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...

We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.

With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The main theorem of (...) the paper (Theorem 2.2) is analogous to the Wroski's result for equational classes of algebras [13]. It reads that for a large class of logics the conjunction of (AP) and (FEP) is equivalent to (IT) and that the latter property is equivalent to (MIP). (shrink)

This article attempts to answer the question: what has the current migration crisis revealed in relations between Christianity and Islam, two religions with common Abrahamic roots? What conclusions can be drawn about the state of these relations, particularly with regard to ordinary members of the two religions? How should we assess the reaction of Christians in Europe to the inflow of refugees from Muslim countries in the light of the Gospel, the Second Vatican Council and the teaching of Pope Francis?The (...) article consists of four parts. Part I briefly presents Christian-Muslim relationships over the centuries. Part II focuses on the sense of danger occurring in European societies in connection with the influx of Muslims during the migration crisis. Part III presents the teachings of the Second Vatican Council about Islam and Part IV describes Pope Francis’s attitude towards refugees from Muslim countries. (shrink)

From the perspective of Marek J. Siemek’s theory of modernity, one of the most important problem is to include conflicts into institutional framework of the modern society. He reinterprets Hegel’s dialectics of the struggle for recognition by conceptual tools of Hobbes and Marx in order to uncover hidden assumptions and conditions of possibility of the social rationality. For Siemek, law as purely formal, autopoetic social system or social subject, which produces individual subjects, is the first of the conditions of possibility (...) of modernity. The second one is the convergence of formal and material presuppositions of law—or, speaking generally—the convergence of form and content of the social reason. Form and content, facticity and normativity, instrumentality and communicativity are aspects of the process of rationalization andof the only one reason, self-generating in the history. So for Siemek, the Hegelian model of the struggle for recognition gains its theoretical power only when it is interpreted from the perspective of economical, technical and legal rationalization of modernity. Only such perspective is able to construct “the transcendental social philosophy” which starts from critique of “the non-instrumental reason”. (shrink)

The aim of the article is to present the attempts of establishing institutions of a system of worker’s self-management in the selected countries of the so-called real socialism system in Eastern Europe. The analysis considers three of those countries, namely Yugoslavia, Poland and Hungary, whose experiences in participation of the employees’ implementation were the most significant. Particular attention was paid to the evolution of socialist regimes approach to workers’ self-management. The paper tries to answer the question whether workers’ self-management posed (...) a threat to the socialist regimes persistence. The research method used in the study is an indepth survey and analysis of literature and legal acts. (shrink)

Discursive (or discussive) logic, D₂, introduced by Jaśkowski, is widely recognized as a first formal approach to paraconsistency. Jaśkowski applied a quite extraordinary technique at that time to describe his logic. He neither gave a set of the axiom schemata nor presented a direct semantics for D₂ but used a translation function to express his philosophical and logical intuitions. Discursive logic was defined by an interpretation in the language of S₅ of Lewis. The aim of this paper is to present (...) a modified system of the discursive logic that allows some of the weaker versions of Duns Scotus's thesis to be valid. The initial idea is to consider a different characteristic of the connective of negation. We introduce both a direct semantics and an axiomatization of the new system, prove the key metatheorems, and describe labeled tableaux for the system. (shrink)

In 1948, Stanis aw Ja kowski defined a logical system D2 of a discursive 1 sentential calculus. The aim of this paper is to introduce the reader to the basic ideas of the discursive logic and to show, in a historical perspective, its development originating from the two germ papers [19] and [20]. We intend to present some problems connected with it and outline the solutions they have received up to the present day.

We prove that if f is a partial Borel function from one Polish space to another, then either f can be decomposed into countably many partial continuous functions, or else f contains the countable infinite power of a bijection that maps a convergent sequence together with its limit onto a discrete space. This is a generalization of a dichotomy discovered by Solecki for Baire class 1 functions. As an application, we provide a characterization of functions which are countable unions of (...) continuous functions with domains of type Πn0, for a fixed n<ω. For Baire class 1 functions, this generalizes analogous characterizations proved by Jayne and Rogers for n=1 and Semmes for n=2. (shrink)

Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.