Study in the period of coronavirus disease 2019 lockdown and the effect of different exercise training programs on the quality of life dimension are limited. This randomized control study as a part of which the impact of an 8-week neuromuscular training program on the 90 healthy young individuals’ QoL after COVID-19 lockdown was assessed using a short form of the WHOQOL-BREF questionnaire comprising of four domains. The intervention group took part in a neuromuscular training program consisting of dynamic neuromuscular stabilization (...) and whole-body vibration training. In contrast, the control group did not participate in any programmed physical activity. From pre- to post-intervention test, the NT group significantly and substantially improved [mean change ] all the QoL domains, physical for 12.78 scores, psychological for 13.12 scores, social relationships for 20.57 scores, and environmental for 24.40 scores. These results suggest that the NT program could enhance QoL in young and healthy participants following COVID-19 lockdown. (shrink)

Split preorders are preordering relations on a domain whose composition is defined in a particular way by splitting the domain into two disjoint subsets. These relations and the associated composition arise in categorial proof theory in connection with coherence theorems. Here split preorders are represented isomorphically in the category whose arrows are binary relations and whose composition is defined in the usual way. This representation is related to a classical result of representation theory due to Richard Brauer.

It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in terms of natural transformations equipped with “graphs” (g-natural transformations) and corresponding morphism theorems are given as consequences. Using these results, some basic relations between the free categories of these classes are obtained.

It is proved that equations between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equation in the language of free cartesian categories collapses a cartesian category into a preorder. An analogous result holds for categories with binary products, which may lack a terminal object. The proof is based on a coherence result for cartesian categories, which is related to model-theoretic methods of normalization. This maximality of cartesian categories, which is analogous to Post (...) completeness, shows that the usual equivalence between deductions in conjunctive logic induced by βη normalization in natural deduction is chosen optimally. (shrink)

It is proved that MacLane''s coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in terms of natural transformations equipped with graphs (g-natural transformations) and corresponding morphism theorems are given as consequences. Using these results, some basic relations between the free categories of these classes are obtained.

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference. This paper examines in the (...) setting of categorial proof theory the conjecture that two derivations with the same premises and conclusions stand for the same proof if and only if they have the same generality. For that purpose generality is defined within a category whose arrows are equivalence relations on finite ordinals, where composition is rather complicated. Several examples are given of deductive systems of derivations covering fragments of logic, with the associated map into the category of equivalence relations of generality. This category is isomorphically represented in the category whose arrows are binary relations between finite ordinals, where composition is the usual simple composition of relations. This representation is related to a classical representation result of Richard Brauer. (shrink)

Članek je posvečen vprašanju, katere vire je pri pisanju svoje Cerkvene zgodovine oziroma dodatka k prevodu Evzebijevega istoimenskega dela uporabljal Rufin iz Akvileje. Iz samega besedila izhaja, da je upora­bljal tako ustne kot pisne vire, pri čemer Rufin prve večkrat navaja, drugih pa skorajda ne. Kljub temu je danes moč zanesljivo reči, da se je pri pisanju opiral na številne tako latinske kot grške vire. Rufinov ugled na področju (cerkvene) zgodovine je v zadnjem stoletju precej omajala teza, da je za (...) večji del svojega dodatka enostavno prevedel danes izgubljeno cerkveno zgodovino Gelazija iz Cezareje. Ker naj bi bilo vsebino slednje moč rekonstruirati iz kasnejših grških virov, je Rufinov dodatek v strokovnih krogih deležen manj pozornosti, kot si kljub svojim pomanjkljivostim zasluži. Članek se tako osredotoča predvsem na dva vidika Rufinovih pisnih virov — na vprašanje njegove odvisnosti od Gelazija in na vprašanje, za katere pisne vire dejansko lahko rečemo, da jih je uporabljal. (shrink)

Warren Buckland _The Cognitive Semiotics of Film_ Cambridge: Cambridge University Press, 2000 ISBN: 0-521-78005-5 (hb) xi +174 pp.

This article discusses the significance of social capital in Bourdieu-inspired analyses of contemporary South-East European societies. We first recapitulate Bourdieu?s theorization of social capital, emphasizing that it allows different operationalizations expressly because of its rather abstract theoretical character. Following that, we explain what is meant by?South- East European societies? and that their inequality-generating mechanisms are largely based on social closure. In the central part of the article, we comment on some attempts at operationalization of social capital in the SEE region. (...) While we also discuss two cases of eclectically mixing Lin?s operationalization with Bourdieusian concepts, at the center of our attention is the elaboration of Bourdieu?s theorization of social capital put forward by the Serbian sociologist Predrag Cveticanin. The relevance of his concepts of?social capital of solidarity? and?social capital of informal connections? for the study of class relations in post-socialist societies in South-East Europe highlights the advantages of a consistent application of the Bourdieusian framework in a contemporary context. (shrink)

It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in terms of natural transformations equipped with “graphs” (g-natural transformations) and corresponding morphism theorems are given as consequences. Using these results, some basic relations between the free categories of these classes are obtained.

An extension of the notion of dinatural transformation is introduced in order to give a criterion for preservation of dinaturality under composition. An example of an application is given by proving that all bicartesian closed canonical transformations are dinatural. An alternative sequent system for intuitionistic propositional logic is introduced as a device, and a cut-elimination procedure is established for this system.

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric strictly monoidal categories, where associativity arrows are identities. Mac Lane's pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degenerate case of Mac Lane's hexagonal condition for commutativity. This decomposition is analogous to the derivation of the Yang-Baxter equation from Mac Lane's hexagon and the naturality of commutativity. The pentagon (...) is reduced to an inductive definition of a kind of commutativity. (shrink)

Coherence is demonstrated for categories with binary products and sums, but without the terminal and the initial object, and without distribution. This coherence amounts to the existence of a faithful functor from a free category with binary products and sums to the category of relations on finite ordinals. This result is obtained with the help of proof-theoretic normalizing techniques. When the terminal object is present, coherence may still be proved if of binary sums we keep just their bifunctorial properties. It (...) is found that with the simplest understanding of coherence this is the best one can hope for in bicartesian categories. The coherence for categories with binary products and sums provides an easy decision procedure for equality of arrows. It is also used to demonstrate that the categories in question are maximal, in the sense that in any such category that is not a preorder all the equations between arrows involving only binary products and sums are the same. This shows that the usual notion of equivalence of proofs in nondistributive conjunctive-disjunctive logic is optimally defined: further assumptions would make this notion collapse into triviality. (shrink)

Coherence is demonstrated for categories with binary products and sums, but without the terminal and the initial object, and without distribution. This coherence amounts to the existence of a faithful functor from a free category with binary products and sums to the category of relations on finite ordinals. This result is obtained with the help of proof-theoretic normalizing techniques. When the terminal object is present, coherence may still be proved if of binary sums we keep just their bifunctorial properties. It (...) is found that with the simplest understanding of coherence this is the best one can hope for in bicartesian categories. The coherence for categories with binary products and sums provides an easy decision procedure for equality of arrows. It is also used to demonstrate that the categories in question are maximal, in the sense that in any such category that is not a preorder all the equations between arrows involving only binary products and sums are the same. This shows that the usual notion of equivalence of proofs in nondistributive conjunctive-disjunctive logic is optimally defined: further assumptions would make this notion collapse into triviality. (shrink)

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference.This paper examines in the setting (...) of categorial proof theory the conjecture that two derivations with the same premises and conclusions stand for the same proof if and only if they have the same generality. For that purpose generality is defined within a category whose arrows are equivalence relations on finite ordinals, where composition is rather complicated. Several examples are given of deductive systems of derivations covering fragments of logic, with the associated map into the category of equivalence relations of generality.This category is isomorphically represented in the category whose arrows are binary relations between finite ordinals, where composition is the usual simple composition of relations. This representation is related to a classical representation result of Richard Brauer. (shrink)

Coherence with respect to Kelly–Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this result, coherence is first established for categories that correspond to the multiplicative conjunction–disjunction fragment with first-order quantifiers of classical linear logic, a fragment lacking negation. These results extend results of [K. Došen, Z. Petrić, Proof-Theoretical Coherence, KCL Publications , London, 2004 ; K. Došen, Z. Petrić, Proof-Net Categories, (...) Polimetrica, Monza, 2007 ], where coherence was established for categories of the corresponding fragments of propositional classical linear logic, which are related to proof nets, and which could be described as star-autonomous categories without unit objects. (shrink)

This paper presents a coherence theorem for star-autonomous categories exactly analogous to Kelly and Mac Lane’s coherence theorem for symmetric monoidal closed categories. The proof of this theorem is based on a categorial cut-elimination result, which is presented in some detail.

A split preorder is a preordering relation on the disjoint union of two sets, which function as source and target when one composes split preorders. The paper presents by generators and equations the category SplPre, whose arrows are the split preorders on the disjoint union of two finite ordinals. The same is done for the subcategory Gen of SplPre, whose arrows are equivalence relations, and for the category Rel, whose arrows are the binary relations between finite ordinals, and which has (...) an isomorphic image within SplPre by a map that preserves composition, but not identity arrows. It was shown previously that SplPre and Gen have an isomorphic representation in Rel in the style of Brauer.The syntactical presentation of Gen and Rel in this paper exhibits the particular Frobenius algebra structure of Gen and the particular bialgebraic structure of Rel, the latter structure being built upon the former structure in SplPre. This points towards algebraic modelling of various categories motivated by logic, and related categories, for which one can establish coherence with respect Rel and Gen. It also sheds light on the relationship between the notions of Frobenius algebra and bialgebra. The completeness of the syntactical presentations is proved via normal forms, with the normal form for SplPre and Gen being in some sense orthogonal to the composition-free, i.e. cut-free, normal form for Rel. The paper ends by showing that the assumptions for the algebraic structures of SplPre, Gen and Rel cannot be extended with new equations without falling into triviality. (shrink)

It is proved that all the isomorphisms in the cartesian category freely generated by a set of objects (i.e., a graph without arrows) can be written in terms of arrows from the symmetric monoidal category freely generated by the same set of objects. This proof yields an algorithm for deciding whether an arrow in this free cartesian category is an isomorphism.

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation, those of an equivalence relation, and other properties appropriate for an equality relation in linear logic. The guiding idea is that equality of proofs is induced by coherence, understood as the existence of a faithful functor from a syntactical category into a category whose arrows (...) correspond to diagrams. Edges in these diagrams join occurrences of variables that must remain the same in every generalization of the proof. It is found that assumptions about equality of proofs for equality are parallel to standard assumptions about equality of arrows in categories. They reproduce standard categorial assumptions on a different level. It is also found that assumptions for a preordering relation involve an adjoint situation. (shrink)

It is shown that all the assumptions for symmetric monoidal categories follow from a unifying principle involving natural isomorphisms of the type →, called medial commutativity. Medial commutativity in the presence of the unit object enables us to define associativity and commutativity natural isomorphisms. In particular, Mac Lane’s pentagonal and hexagonal coherence conditions for associativity and commutativity are derived from the preservation up to a natural isomorphism of medial commutativity by the biendofunctor . This preservation boils down to an isomorphic (...) representation of the Yang–Baxter equation of symmetric and braid groups. The assumptions of monoidal categories, and in particular Mac Lane’s pentagonal coherence condition, are explained in the absence of commutativity, and also of the unit object, by a similar preservation of associativity by the biendofunctor . In the final section one finds coherence conditions for medial commutativity in the absence of the unit object. These conditions are obtained by taking the direct product of the symmetric groups for 0≤i≤n. (shrink)

It is proved that all the isomorphisms in the cartesian category freely generated by a set of objects can be written in terms of arrows from the symmetric monoidal category freely generated by the same set of objects. This proof yields an algorithm for deciding whether an arrow in this free cartesian category is an isomorphism.

A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.

Prethodno, u izlaganju »Petrić i Acastos«, održanom na simpoziju Petrić i renesansne filozofske tradicije 2008. godine, ustanovili smo da je Petrić najbliži platonovsko-novoplatonovsko- pitagorovskom izvorniku, ali je pridonio raščinjavanju klasične etičke vrline , da je vrlo blizak drugom modelu za uspoređivanje, Acastosu I i donekle se približava Acastosu II .S istim trima modelima sada prelazimo na usporedbu u odnosu na pjesničko umijeće, kako je izloženo u petnaest izabranih Petrićevih tekstova u knjizi Ljerke Schiffler Frane Petrić o pjesničkom umijeću . Pitat (...) ćemo se koliko se u navedenoj usporedbi otkrilo, manje ili više, bliskosti s prethodnim zaključcima.Dakako, usput će se pokušati ustanoviti je li Petrićeva poetika samo obrana Platonove linije ili sadržava i neke elemente aristotelizma, što ga ne bi povezalo samo s barokom i manirizmom nego i s modernom estetikom.The author established on the occasion of the previous presentation “Petrić and Acastos” given at the symposium Petrić and Renaissance Philosophical Traditions, held in 2008, that Petrić was closest to the Platonist-Neoplatonist-Pythagorean original, but also that he contributed to the disintegration of classical ethical virtue and that there were two more comparative models he came close to – that of Acastos I and to some extent that of Acastos II .Retaining the three models, the author now deals with the comparison in relation to poetic art as it is outlined in the fifteen selected Petrić’s texts in the book by Ljerka Schiffler entitled Frane Petrić o pjesničkom umijeću . The author will look into the degree to which the mentioned comparison revealed connections with previous conclusions.Needless to say, the author will along the way try to determine whether Petrić’s poetics presents merely a defence of Plato’s attitude or it contains some elements of Aristotelianism, which would connect Petrić with not only Baroque and Mannerism but also modernist aesthetics. (shrink)

U četiri djela objavljena do 1562. godine, Frane Petrić tematizira vrlinu i sreću. Osnovna tema prvog Petrićeva djela, La città felice, jest postizanje sreće putem vrline. Ostala tri Petrićeva djela u kojima se tematizira vrlina ili sreća su Il Barignano. Dialogo dell’honore, Della historia diece dialoghi i Della retorica dieci dialoghi. U navedenim su djelima vrlina i sreća teme kojih se Petrić dotiče samo usput. U Barignanu, dijalogu o časti, tematizira se odnos vrline i časti. Deset dijaloga o povijesti donosi (...) nam kratku raspravu o ostvarenju sreće, kao podtemu raspravi o svrsi povijesti. U Deset dijaloga o retorici Petrić kratko raspravlja o povezanosti pohvale i vrline te o različitosti izvora vrline i dobra. Petrić je pisao kako mu je cilj slijediti božanskog Platona, međutim, u navedena četiri djela, barem što se tiče vrline i sreće, ostaje vjeran Aristotelu i njegovim učenjima iz Politike, Nikomahove etike i Retorike.In the four works published up to the year 1562, Frane Petrić discusses virtue and happiness. The basic theme of his first book, La città felice, is how to achieve happiness through virtue. The other three works in which Petrić deals with virtue and happiness are Barignano. Il Dialogo dell’honore, Della historia diece dialoghi and Della retorica dieci dialoghi. In these works, the issues of virtue and happiness are just collateral issues. In Barignano, dialogue of honor, Petrić discusses the relationship between virtue and honor. In della historia Petrić brings us a short discussion on the achievement of happiness, as a subtopic in the discussion about the purpose of history. In della retorica Petrić briefly discusses the connection between praise and virtues, as well as the diversity of sources of virtues and good. Petrić wrote that his goal is to follow the divine Plato; however, in these four works he is still loyal to Aristotle – at least regarding the issues of virtue and happiness – and his teachings from Politics, The Nicomachean Ethics and Rhetoric. (shrink)

U članku se analizira Petrićeva usporedba Aristotelove podjele na supralunarni i sublunarni svijet s morskim bićem koje Petrić naziva Marinus Glaucus. Tu usporedbu, s bićem koje je dijelom riba, a dijelom kamen, rabi Petrić kako bi eksplicirao neprirodnost, monstruoznost spomenute Aristotelove podjele. Postavlja se pitanje što je ili tko je Marinus Glaucus. U članku se izlaže da Petrićev Marinus Glaucus najvjerojatnije u sebi ujedinjava i svojstva grčko-rimskog morskog polubožanstva koje se zove Glauko i osobine jedne vrste otrovnih riba koje se (...) u nekim europskim jezicima zovu kamene ribe, a svojstvena im je mimikrija, prilagodba okolišu u kojem žive, kamenu.Im Aufsatz wird der Petrić´s Vergleich der Aristotelischen Aufteilung in die sublunare und supralunare Welt, mit einem Wesen, das er als Marinus Glaucus bezeichnet, analisiert. Diesen Vergleich mit dem Wesen, das er als halb Fisch, halb Stein bestimmt, unternimmt Petrić um die Widernatürlichkeit, ja Monstruosität der genannten Aristotelischen Aufteilung darzulegen. Es wird die Frage gestellt, was, oder, wer ist Marinus Glaucus. Es wird vermutet, dass Petrić’s Marinus Glaucus zwei verschiedene Beschaffenheiten in sich birgt: die einer griechisch-römischen Halbgottheit namens Glauco und die einer Art giftigen Mittelmeerfische, die in einigen europäischen Sprachen Steinfische heißen und die eine Mimikry auszeichnet, die Fähigkeit sich der Welt in der sie leben, dem steinigen Meerboden, anzugleichen. (shrink)