Infinitary action logic can be naturally expanded by adding exponential and subexponential modalities from linear logic. In this article we shall develop infinitary action logic with a subexponential that allows multiplexing (instead of contraction). Both non-commutative and commutative versions of this logic will be considered, presented as infinitary sequent calculi. We shall prove cut admissibility for these calculi, and estimate the complexity of the corresponding derivability problems: in both cases it will turn out to be between complete first-order arithmetic and (...) the \(\omega ^\omega \) level of the hyperarithmetical hierarchy. Here the complexity upper bound is much lower than that for the system with a subexponential that allows contraction. The complexity lower bound in turn is much higher than that for infinitary action logic. (shrink)

The Ukrainian legislator’s differentiation of criminal liability for certain manifestations of collaboration has led to unjustified competition and considerable difficulties in qualifying the relevant unlawful acts. The purpose of this study was to analyse the specific features of criminal liability for aiding and abetting the aggressor state in the national and international dimensions. To complete the tasks of this study, a set of scientific methods was employed: dogmatic – in the analysis of legal constructions of elements of collaboration and abetting (...) the aggressor state; comparative legal – in the context of comparing the rules on liability for collaboration and the rules of international humanitarian law. The study showed that Ukrainian criminal law theory and court practice have not developed consistent approaches to the application of the rules on liability for collaboration. The study focused on the fact that the criminal legislation of Ukraine applies an approach whereby certain types of economic collaboration are factually identified with military collaboration, which does not follow international humanitarian law. It was concluded that when qualifying the transfer of material resources to representatives of the aggressor state, there is a competition between the provisions of Part 4 of Article 111- 1 and Article 111-2 of the Criminal Code of Ukraine. In such a situation, it is reasonable to apply the rule on liability for collaboration. It was found that the payment of taxes, fees, and other mandatory payments to the Russian budget of any level, made in the occupied territory of Ukraine by a citizen of Ukraine, a foreigner, a stateless person for themselves and/or in the interests of legal entities registered in the territory of the Russian Federation cannot be covered by the objective side of abetting the aggressor state, as it does not follow international humanitarian law and does not contain such a feature as voluntariness, which is a mandatory feature of the crime under Article 111-2 of the Criminal Code of Ukraine. The practical significance of this study lies in defining certain rules for qualifying aiding and abetting the aggressor state which may be used by pre-trial investigation authorities in the legal assessment of such behaviour. (shrink)

We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an$\omega $-rule, and prove that the derivability problem in this calculus is$\Pi _1^0$-hard. This solves a problem left open by Buszkowski (2007), who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a Lambek grammar with (...) unique type assignment, without Lambek’s nonemptiness restriction imposed (cf. Safiullin, 2007). (shrink)

In the original publication, the affiliation of the author Max Kanovich was processed incorrectly. It has been updated in this correction.

We consider language models for the Lambek calculus that allow empty antecedents and enrich them with constants for the empty language and for the language containing only the empty word. No complete calculi are known with respect to these semantics, and in this paper we consider several trivalent systems that arise as fragments of these models? logics.

We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill’s calculi, and focus on their fragments including multiplicative (Lambek) connectives, additive conjunction and disjunction, brackets and bracket modalities, and the! subexponential modality. For both systems, we resolve issues connected with the cut rule and provide necessary modifications, after which we prove admissibility of cut (cut elimination theorem). We also prove (...) algorithmic undecidability for both calculi, and show that categorial grammars based on them can generate arbitrary recursively enumerable languages. (shrink)

L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic \ has exactly 5 pretabular extensions PM1–PM5. In this paper, we study the problem of unification for all given logics. We showed that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification. Complete sets of unifiers in logics are described.

We give a systematic method of constructing extensions of the Kuznetsov-Gerčiu logic KG without the finite model property (fmp for short), and show that there are continuum many such. We also introduce a new technique of gluing of cyclic intuitionistic descriptive frames and give a new simple proof of Gerčiu’s result [9, 8] that all extensions of the Rieger-Nishimura logic RN have the fmp. Moreover, we show that each extension of RN has the poly-size model property, thus improving on (...) [9]. Furthermore, for each function f: omega -> omega, we construct an extension Lf of KG such that Lf has the fmp, but does not have the f-size model property. We also give a new simple proof of another result of Gerčiu [9] characterizing the only extension of KG that bounds the fmp for extensions of KG. We conclude the paper by proving that RN.KC = RN + (¬p vee ¬¬p) is the only pre-locally tabular extension of KG, introduce the internal depth of an extension L of RN, and show that L is locally tabular if and only if the internal depth of L is finite. (shrink)

April 29-30, 1995 in the premises of the Ternopil Medical Institute. Academician I.Ya.Gorbachevsky held an international scientific conference with such a title. In her work participated: A. Kolodny, - deputy director of the Institute of Philosophy of the National Academy of Sciences of Ukraine, President of the Ukrainian Association of Religious Studies; Employees of the Institute of Philosophy of the National Academy of Sciences of Ukraine - V.Malakhov, V.Klimov, L.Filipovich, O.Sagan, V.Demian, T.Chaika; Lviv Museum of the History of Religion - (...) G. Skop-Drusyuk, L. Skop, I. Petrov; Ternopil universities and institutions Y.Sudersky, O.Gudim, L. Boytsun, and others. Our fellow countryman, Professor Stepan Yarmus, participated in the conference. (shrink)

Quantum electrodynamics is the theory of electrons and other elementary charged particles, interacting through the exchange of light quanta. Albert Einstein introduced the light quantum in 1905, but for about three decades physicists applied quantum ideas mainly in theories of the structure and behavior of matter, not to electromagnetic radiation itself, which was always treated semi-classically. This began to change after 1923 with the discovery of the Compton effect and its kinematic description by Arthur Compton and Peter Debye, based on (...) the light quantum. In this paper we review the study of high-energy radiation that led to Compton's discovery. We discuss the analysis of the intensity distribution of Compton-scattered radiation that together with the ''new'' quantum theory beginning in 1925, resulted in the development, especially by Pascual Jordan and Paul Dirac, of a quantum theory of electromagnetic radiation in interaction with matter. (shrink)

I consider and reject four possible arguments directed against the preservation of natural aesthetic conditions. (1) Beauty is not out there in nature, but is “in the eye ofthe beholder.” I argue that since ingredients ofnature cause aesthetic experiences, we cannot justifiably disregard and exploit nature. Preservation of aesthetic conditions is compatible with both objective and nonobjective theories of aesthetic value. (2) Frequent aesthetic disagreements bring about irresolvable disputes concerning which segments of nature to preserve. I claim that these disputes (...) are not irresolvable. Not all disputes about nature’s aesthetic values are purely aesthetic disputes: ecological balance, community identity, historic continuity, and economics are relevant; aesthetic experts can help; and such disputes can be put to a vote. (3) Natural beauty is not important compared to nonaesthetic values of nature. I show that this is questionable. Current awareness of environmental problems includes a rapidly growing concern for natural aesthetics. Moreover, even if majority preference is for nonaesthetic uses of nature, this does not settle the question of whether we ought to preserve nature’s attractive features. (4) From neither a utilitarian nor a deontological viewpoint do we have an obligation to preserve natural aesthetic conditions for future generations. I argue that even if we do not have a strict obligation, it does not follow that it makes no moral difference whether we preserve. Not yet existing people may have no rights against us, but this does not mean that we do no wrong in polluting and destroying aesthetic conditions of the natural world in which future people will live. (shrink)

The word ‘existentialism’ has become something of a catchword in religious circles today, and one suspects that it is sometimes a substitute rather than a medium for thought. Most theological teachers must from time to time have received from a pupil an essay in which the words ‘existential’, ‘existentially’ and ‘existentialism’ appear to have been sprinkled from a pepper-pot over an exposition whose meaning would remain unchanged if these words were excised altogether. Nevertheless, usum non tollit abusus, and the following (...) rather unsystematic remarks may perhaps be of some help in elucidating and evaluating a mode of thought and expression which has attracted the interest of some of the more profound, as well as of some of the more superficial, theological and philosophical writers of the present day. (shrink)

The distance in conceptual space between the philosophical pragmatism of William James and the narrative theologies of Hans Frei and Stanley Hauerwas would appear at first glance to be significant. Hauerwas himself has measured that distance in public, when his extended critique of James supplied a good portion of the agenda for his Gifford Lectures, delivered in 2001 at St. Andrews and subsequently published as With the Grain of the Universe: The Church's Witness and Natural Theology. In this book, Jacob (...) Goodson dramatically closes the distance, appealing consistently to James's pragmatism as a resource not only for understanding the thought of contemporary narrative theologians but also for productively... (shrink)

Preliminary Material /Louis M. Epstein --Polygamy /Louis M. Epstein --Concubinage /Louis M. Epstein --Levirate Marriage /Louis M. Epstein --Intermarriage /Louis M. Epstein --Incest /Louis M. Epstein --Other Marriage Prohibitions /Louis M. Epstein --Abbreviations /Louis M. Epstein --Register of Foreign Terms /Louis M. Epstein --Bibliography /Louis M. Epstein --Index of Subjects and Names /Louis M. Epstein.

Abū Ishāq al-Isfarāyīnī (d. 418/1027) was one of the prominent figures of Khorasan Shafiʻīsm and a jurist among the Aṣḥāb al-Wujūh. He received education in Irāq from important scholars in the fields of theology (kalām), jurisprudence (fiqh), principles of jurisprudence (usul al-fiqh), and hadīth. After returning to Nishabur, he taught at a madrasa built in his name. He trained students such as ʿAbd al-Qāhir al-Baghdādī (d. 429/1037-38), Abū al-Ṭayyib al-Ṭabarī (d. 450/1058), Abu al-Qāsim al-Isqāf al-Isfarāyīnī (d. 452/1060), Abu al-Rabīʿ Ilākī (...) (d. 465/1073), and Abu al-Qāsim al-Qushayrī (d. 465/1072), who later influenced the course of Shāfiʿīsm. He authored works as an important hadith scholar and Ashʿarī theologian. Although most of these works have not survived to the present day, we learn about his views through excerpts from them. He held views, reflected in the prin-ciples of jurisprudence, that led to criticism for being influenced by the Muʿtazila. Despite being a theologian, his adoption of the jurists' method in jurisprudence further emphasizes the importance of his views. The aim of this study is to reveal Abū Ishāq al-Isfarāyīnī's thoughts on the principles of jurisprudence, specifically in the areas of hadīth, consensus (ijmā), indepen-dent reasoning (ijtihād), and imitation (taqlīd), and to identify their reflecti-ons on the Shāfiʿī school of jurisprudence. Since there is no specific study on Abū Ishāq al-Isfarāyīnī’s thoughts on jurisprudence in our country, we beli-eve that this research will contribute to future studies on his legal scholarship. (shrink)

The question addressed here is whether evidence concerning defendants' past criminal records should be introduced at their trials because such evidence reveals their character and thus reveals whether they are the kinds of persons likely to have committed the crimes with which they are currently charged. I strongly caution against the introduction of such evidence for a number of reasons. First, the link between defendants' past criminal records and claims about their standing dispositions to think and act is tenuous, at (...) best. Second, noncharacter, or trace, evidence should have primacy in determining the guilt or innocence of defendants. Third, character evidence will vary in its freshness and specificity. Other things being equal, only relatively fresh and specific character evidence has probative value. Moreover, such evidence will have greater probative value in criminal cases where the issue before the court is whether a crime has been committed than in cases where the issue is whether it was the defendant who committed the crime. Finally, we might be more sanguine about the introduction of fresh and specific character evidence under conditions likely to work against its misuse or misinterpretation. However, the relevant conditions may not often be satisfied in the real world of criminal trials and defendants. (shrink)