Logic of classical refutability and class of extensions of minimal logic

This article continues the investigation of paraconsistent extensions of minimal logic Lj started in [6, 7]. The name “logic of classical refutability” is taken from the H.Curry monograph [1], where it denotes the logic Le obtained from Lj by adding the Peirce law

“Reductio ad absurdum” and Łukasiewicz’s modalities

The present article contains part of results from my lecture delivered at II Flemish-Polish workshop on Ontological Foundation of Paraconsistency

Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch

We consider modified $f(R)$ gravity which may unify $R^m$ early-time inflation with late-time $\Lambda$CDM epoch. It is shown that such model passes the local tests (Newton law, stability of Earth-like gravitational solution, very heavy mass for additional scalar degree of freedom) and suggests the realistic alternative for General Relativity. Various scenarios for future evolution of $f(R)$ $\Lambda$CDM era are discussed.Comment: LaTeX 10 pages, version to appear in PR

On algorithmic properties of propositional inconsistency-adaptive logics

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuNr and CLuNm , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively

The lattice of Belnapian modal logics: Special extensions and counterparts

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on:• introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics;• assigning to every normal modal logic three special conservative extensions in these classes;• associating with every Belnapian modal logic its explosive, complete and classical counterparts.We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK

From the Guest Editors

On the 28th of October, 2006, Alexander Vladimirovich Kuznetsov, so is his full name, would have turned 80. Although belated, the editorial board of Logic and Logical Philosophy, we, the editors and contributors of the present issue, and other members of the logic community mark this event with the present issue. Most of those who contributed to it knew Kuznetsov in person and/or were influenced by him or by his ideas, which very often resided in somebody else’s papers or became part of a scientific folklore. But, to be sure, there are even more mathematicians and logicians who have been witnesses to his scientific activity and/or have taken advantage of its results

On Definability of Connectives and Modal Logics over FDE

The present paper studies two approaches to the expressiveness of propositional modal logics based on first-degree entailment logic, FDE. We first consider the basic FDE-based modal logic BK and certain systems in its vicinity, and then turn to some FDE-based modal logics in a richer vocabulary, including modal bilattice logic, MBL. On the one hand, model-theoretic proofs of the definability of connectives along the lines of [McCullough, “Logical connectives for intuitionistic propositional logic”, Journal of Symbolic Logic 36, 1 (1971): 15–20. DOI: 10.2307/2271511] and [[17] Wansing, “Logical connectives for constructive modal logic”, Synthese 150, 3 (2006): 459–482. DOI: 10.1007/s11229-005-5518-5] are given for various FDE-based modal logics. On the other hand, building on [Odintsov and Wansing, “Disentangling FDE-based paraconsistent modal logics, Studia Logica 105, 6 (2017): 1221–1254. DOI: 10.1007/s11225-017-9753-9], expressibility is considered in terms of mutual faithful embeddability of one logic into another logic. A distinction is drawn between definitional equivalence, which is defined with respect to a pair of structural translations between two languages, and weak definitional equivalence, which is defined with respect to a weaker notion of translations. Moreover, the definitional equivalence of some FDE-based modal logics is proven, especially the definitional equivalence of MBL and a conservative extension of the logic BK□×BK□, which underlines the central role played by BK among FDE-based modal logics

ДО ПИТАННЯ ОБМІНУ ДОСВІДОМ: КУЛЬТУРА І НАУКА БЕЗ КОРДОНІВ

У статті описано важливість обміну досвідом між навчальними закладами. Відображено досвід поширення знань уконтексті історичного розвитку медичної освіти в Україні

Conformal anomaly for 2d and 4d dilaton coupled spinors

We study quantum dilaton coupled spinors in two and four dimensions. Making classical transformation of metric, dilaton coupled spinor theory is transformed to minimal spinor theory with another metric and in case of 4d spinor also in the background of the non-trivial vector field. This gives the possibility to calculate 2d and 4d dilaton dependent conformal (or Weyl) anomaly in easy way. Anomaly induced effective action for such spinors is derived. In case of 2d, the effective action reproduces, without any extra terms, the term added by hands in the quantum correction for RST model, which is exactly solvable. For 4d spinor the chiral anomaly which depends explicitly from dilaton is also found. As some application we discuss SUSY Black Holes in dilatonic supergravity with WZ type matter and Hawking radiation in the same theory. As another application we investigate spherically reduced Einstein gravity with 2d dilaton coupled fermion anomaly induced effective action and show the existence of quantum corrected Schwarszchild-de Sitter (SdS) (Nariai) BH with multiple horizon.Comment: LaTeX file, 15 page

Quantum evolution of Schwarzschild-de Sitter (Nariai) black holes

We calculate the one-loop effective action for conformal matter (scalars, spinors and vectors) on spherically symmetric background. Such effective action (in large $N$ approximation and expansion on curvature) is used to study quantum aspects of Schwarzschild-de Sitter black holes (SdS BHs) in nearly degenerated limit (Nariai BH). We show that for all types of above matter SdS BHs may evaporate or anti-evaporate in accordance with recent observation by Bousso and Hawking for minimal scalars. Some remarks about energy flow for SdS BHs in regime of evaporation or anti-evaporation are also done. Study of no boundary condition shows that this condition supports anti-evaporation for nucleated BHs (at least in frames of our approximation). That indicates to the possibility that some pair created cosmological BHs may not only evaporate but also anti-evaporate. Hence, cosmological primordial BHs may survive much longer than it is expected.Comment: Latex file, 20 pages, shortened versio