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.

Since in Heyting Arithmetic all atomic formulas are decidable, a Kripke model for HA may be regarded classically as a collection of classical structures for the language of arithmetic, partially ordered by the submodel relation. The obvious question is then: are these classical structures models of Peano Arithmetic ? And dually: if a collection of models of PA, partially ordered by the submodel relation, is regarded as a Kripke model, is it a model of HA? Some partial answers to these (...) questions were obtained in [6], [3], [1] and [2]. Here we present some results in the same direction, announced in [7]. In particular, it is proved that the classical structures at the nodes of a Kripke model of HA must be models of IΔ1 and that the relation between these classical structures must be that of a Δ1-elementary submodel. MSC: 03F30, 03F55. (shrink)

The great variety of meditation techniques found in different contemplative traditions presents a challenge when attempting to create taxonomies based on the constructs of contemporary cognitive sciences. In the current issue of Consciousness and Cognition, Travis and Shear add ‘automatic self-transcending’ to the previously proposed categories of ‘focused attention’ and ‘open monitoring’, and suggest characteristic EEG bands as the defining criteria for each of the three categories. Accuracy of current taxonomies and potential limitations of EEG measurements as classifying criteria are (...) discussed. (shrink)

The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend |$\textbf {PTEL}$| to axiomatize the corresponding first-order logic.

Rafael Malach is currently a professor in the department of Neurobiology at the Weizmann Institute in Israel. His current research is aimed at understanding how the neuronal circuitry in the human brain translates a stream of sensory stimuli into meaningful perception. Rafael Malach received his PhD in physiological optics from UC Berkeley and did his post-doctorate research at MIT. Originally doing research on the organization of neuronal connections in the primate brain, his focus has recently shifted to the study of (...) the human cerebral cortex using fMRI. Professor Malach has begun this research at Massachusetts General Hospital, exploring a new object-related region called the lateral occipital complex. Since then he expanded this research, studying the human visual cortex using a variety of methods, including adaptation paradigms, backward masking, and more recently naturalistic stimuli--all aimed at deciphering the intriguing link between perceptual experience and brain activity. (shrink)

We study a propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| with both future and past temporal operators, with non-rigid set of agents and the operators for agents’ knowledge and for common knowledge and with probabilities defined on the sets of runs and on the sets of possible worlds. A semantics is given by a class |${\scriptsize{\rm Mod}}$| of Kripke-like models with possible worlds. We prove decidability of |$\textbf {PTEL}$| by showing that checking satisfiability of a formula in |${\scriptsize{\rm Mod}}$| is (...) equivalent to checking its satisfiability in a finite set of finitely representable structures. The same procedure can be applied to the class of all synchronous |${\scriptsize{\rm Mod}}$|-models. We give an upper complexity bound for the satisfiability problem for |${\scriptsize{\rm Mod}}$|⁠. (shrink)

In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak negation. After that, (...) we define Kripke-style semantics based on possible worlds and derive from it many-valued semantics based on truth-functional valuations for these two paraconsistent logics. Finally, we demonstrate that this model-theoretic inference system is adequate—sound and complete with respect to the axiomatic da Costa-like systems for these two logics. (shrink)

Publication date: 28 April 2021 Source: International Letters of Social and Humanistic Sciences Vol. 90 Author: Zoran Mastilo, Nenad Božović, Dejan Mastilo The paper addresses and evaluates the currency board policy and assesses whether the currency board, as a form of monetary policy, is in the function of development of Bosnia and Herzegovina's national economy. In this context, a hypothesis that the currency board provides the foundation for growth and development of a transition economy is being put to the (...) test. To test the hypothesis, the paper compares the movement of economic growth indicators among the countries of South Eastern Europe with the primary focus on Bosnia and Herzegovina. By comparing the obtained results, as well as by applying the correlation and regression analysis, by means of simple linear regression, it is proven that the currency board does not represent an obstacle to economic growth, but is the basis for establishing the stability of the economy and the basis for sustainable growth and development able to adequately respond to shocks. (shrink)

In this paper we consider the class of truth-functional modal many-valued logics with the complete lattice of truth-values. The conjunction and disjunction logic operators correspond to the meet and join operators of the lattices, while the negation is independently introduced as a hierarchy of antitonic operators which invert bottom and top elements. The non-constructive logic implication will be defined for a subclass of modular lattices, while the constructive implication for distributive lattices (Heyting algebras) is based on relative pseudo-complements as in (...) intuitionistic logic. We show that the complete lattices are intrinsically modal, with banal identity modal operator. We define the autoreferential set-based representation for the class of modal algebras, and show that the autoreferential Kripke-style semantics for this class of modal algebras is based on the set of possible worlds equal to the complete lattice of algebraic truth-values. The philosophical assumption is based on the consideration that each possible world represents a level of credibility, so that only propositions with the right logic value (i.e., level of credibility) can be accepted by this world, then we connect it with paraconsistent properties and LFI logics. The bottom truth value in this complete lattice corresponds to the trivial world in which each formula is satisfied, that is, to the world with explosive inconsistency. The top truth value corresponds to the world with classical logics, while all intermediate possible worlds represent the different levels of paraconsistent logics. (shrink)

U svetu arhajskog čoveka -- Kožev--"posthumni" mislilac -- Žan Delimo ili apologija pesimizma -- Pitanje tragedije.

It is argued that the so-called “absolute space-time theory” is inconsistent, in disagreement with some astronomical observations, and improperly titled.

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.

Članak tematizira ulogu kompleksnog mišljenja u razvoju znanstvene spoznaje i mišljenja općenito. Po Vigotskom, kompleksno mišljenje je početna faza u ontogenezi, pa i filogenezi, ljudskog mišljenja i ono je u tom slijedu predpojmovno. Prema istom autoru, ono ima svoju unutarnju genezu koja započinje asocijativnim kompleksima, a završava pseudopojmovima. Kompleksno mišljenje je po svojoj bitifluidno, neograničeno i omogućuje prenošenje značenja. Smatramo da kompleksno mišljenje dolazi do izraza prije svega u uporabi metafora i analogija. Metafore i analogije imaju važnu eksplanatornu i ponekad (...) čak heurističku ulogu u znanstvenom mišljenju. Kompleksno mišljenje dolazi do izražaja na svim razinama i etapama razvoja znanstvenog mišljenja. Metafore mogu biti dijelom kompleksnog mišljenja kao dominantnog načina mišljenja ili u pojmovnoj strukturi kao pomoćni elementi objašnjenja. Analogije predstavljaju izvjesno strukturiranje kompleksnog i pojmovnogmišljenja.Članak tematizira ulogu kompleksnog mišljenja u razvoju znanstvene spoznaje i mišljenja općenito. Po Vigotskom, kompleksno mišljenje je početna faza u ontogenezi, pa i filogenezi, ljudskog mišljenja i ono je u tom slijedu predpojmovno. Prema istom autoru, ono ima svoju unutarnju genezu koja započinje asocijativnim kompleksima, a završava pseudopojmovima. Kompleksno mišljenje je po svojoj bitifluidno, neograničeno i omogućuje prenošenje značenja. Smatramo da kompleksno mišljenje dolazi do izraza prije svega u uporabi metafora i analogija. Metafore i analogije imaju važnu eksplanatornu i ponekad čak heurističku ulogu u znanstvenom mišljenju. Kompleksno mišljenje dolazi do izražaja na svim razinama i etapama razvoja znanstvenog mišljenja. Metafore mogu biti dijelom kompleksnog mišljenja kao dominantnog načina mišljenja ili u pojmovnoj strukturi kao pomoćni elementi objašnjenja. Analogije predstavljaju izvjesno strukturiranje kompleksnog i pojmovnogmišljenja. (shrink)

Publication date: 2 May 2019 Source: Author: Zoran Mastilo Aim of this paper is to, by means of comparative analysis, demonstrate that contemporary pension systems are limitation factors of development of the Republic of Srpska, and that they should be reformed and improved. Ultimately, pension systems should be the basis for development of the Republic of Srpska. They should significantly improve strengthening of financial markets, enhancement of capital markets, higher growth rates of the Republic of Srpska, idecrease of unemployment. (...) Private pension funds are to change the habits and ideas of every future insurance holder, aiming to make the pension rights a matter of concern of every individual, instead being the obligation and ballast of the society. Today, stabile financing of pension systems and their funds is becoming increasingly questionable. A gap is emerging between the area of rights gained by law and financial possibilities for their implementation. Pay-as-you-go systems, i.e. systems of inter-generation solidarityare particularly endangered. Adequate systematization of gathered data, i.e. evidence, should provide conclusions that pension systems are a limitation todevelopment of national economy. This claim is present in underdeveloped and developing countries, with developed economies also facing grave problems. (shrink)

H.m. is the science of the most general laws and root forces in the development of human society. H.m. came into being in the mid-19th century. Its creators were the leaders and ideologists of the working class: Marx and Engels. In founding a new philosophical world view, dialectical materialsm, Marx and Engels applied it to cognition of society, its history and life.

Aristotle?s definition of humans determines his understanding of education in Politics as politikon zo?n. This definition should always be considered together with the other most important Aristotle?s statement about the human being, in which he claims that?man alone of the animals possesses speech?. The ability to speak becomes most important within the specific political partnership, which has at last attained the limit of virtually complete?self-sufficiency?. Contrary to?every household? where the eldest member?gives the law? to sons and spouses, in the city, (...) the?speech is designed to indicate the advantageous and harmful, and the right and wrong?. In sum, justice became political. It always appears like the outcome of an argument or dispute on what is just. We should understand education in the context of the previous statements. Dispute, the keyword of Aristotle?s understanding of education, appears in the first sentence of Politics VIII. Aristotle states that?they dispute? the question of what?constitutes education and what is the proper way to be educated?. There is not one complete, definitive, and standard answer to the question of what is the best way to be educated that we should implement in the educational activities. Based on Aristotle?s view, I claim that the first purpose of education is not to determine and constrain the activity of the youth and citizens in general, but to provoke and facilitate the dispute on the essence and aims of education. (shrink)