Using the Makkai's duality for first-order logic, we characterise effective descent morphisms in 2-categories of pretoposes and Barr-exact categories. In both cases they coincide with conservative morphisms. We show that in those 2-categories the 2-coregular factorisations are exactly quotient-conservative factorisations. We also prove a generalisation of the Makkai duality for pseudoelementary categories.

In the paper [8], the first author developped a topos- theoretic approach to reference and modality. (See also [5]). This approach leads naturally to modal operators on locales (or spaces without points). The aim of this paper is to develop the theory of such modal operators in the context of the theory of locales, to axiomatize the propositional modal logics arising in this context and to study completeness and decidability of the resulting systems.

For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.

In my paper I review the main strategies adopted by two leading schools in cognitive science, symbolic artificial intelligence (AI) and connectionism, in modeling time-dependent phenomena such as learning. In particular, I briefly mention shortcomings of non-monotonic logic approach that dominates symbolic AI. I also discuss the problems that beset the recurrent networks approach advocated by connectionists (e.g., S. Grossberg) and philosophers (e.g., P. Churchland), who focus their attention on oscillatory behavior of such networks. I point out that neither approach (...) adequately captures essential features of the dynamics of human temporal awareness. Finally, I develop certain ideas borrowed from neurophysiologists (e.g., W. Freeman) and system theorists and describe the brain-mind, the entity that is capable of producing temporal awareness, as a self-organizing system that exhibits chaotic dynamics and generates a dynamic structure that resembles the chaotic hierarchy o Rossler. (shrink)

Gelfond and Lifschitz proposed the notion of a stable model of a logic program. We establish that the set of all stable models in a Herbrand universe of a recursive logic program is, up to recursive renaming, the set of all infinite paths of a recursive, countably branching tree, and conversely. As a consequence, the problem, given a recursive logic program, of determining whether it has at least one stable model, is Σ11-complete. Due to the equivalences established in the authors' (...) previous nonmonotone rule systems papers ), this applies equally to truth maintenance systems and default logics. (shrink)

The topos theory gives tools for unified proofs of theorems for model theory for various semantics and logics. We introduce the notion of power and the notion of generalized quantifier in topos and we formulate sufficient condition for such quantifiers in order that they fulfil downward Skolem-Löwenheim theorem when added to the language. In the next paper, in print, we will show that this sufficient condition is fulfilled in a vast class of Grothendieck toposes for the general and the existential (...) quantifiers. (shrink)

This paper is a continuation of the investigation from [13]. The main theorem states that the general and the existential quantifiers are (, -reducible in some Grothendieck toposes. Using this result and Theorems 4.1, 4.2 [13] we get the downward Skolem-Löwenheim theorem for semantics in these toposes.

We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and.

A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...) fp can be derived from that of Sh(P 0 ,J 0 ) via the embedding Φ. We also show that the equivalence relations in HA op fp are not effective in general. On the way to these results we establish a new kind of duality between HA op fp and a category of sheaves equipped with certain structure defined in terms of Ehrenfeucht games. Our methods are model-theoretic and combinatorial as opposed to proof-theoretic as in [Pi]. (shrink)

This paper proposes a unified dependent type analysis of three puzzling phenomena: inversely linked interpretations, weak definite readings in possessives and Haddock-type readings. We argue that the three problematic readings have the same underlying surface structure, and that the surface structure postulated can be interpreted properly and compositionally using dependent types. The dependent type account proposed is the first, to the best of our knowledge, to formally connect the three phenomena. A further advantage of our proposal over previous analyses is (...) that it offers a principled solution to the puzzle of why both inversely linked interpretations and weak definite readings are blocked with certain prepositions. (shrink)

Under some assumptions on an equational theory S , we give a necessary and sufficient condition so that S admits a model completion. These assumptions are often met by the equational theories arising from logic. They say that the dual of the category of finitely presented S-algebras has some categorical stucture. The results of this paper combined with those of [7] show that all the 8 theories of amalgamable varieties of Heyting algebras [12] admit a model completion. Further applications to (...) varieties of modal algebras are given in [8]. (shrink)

A number of nonmonotonic reasoning formalisms have been introduced to model the set of beliefs of an agent. These include the extensions of a default logic, the stable models of a general logic program, and the extensions of a truth maintenance system among others. In [13] and [16], the authors introduced nonmonotomic rule systems as a nonlogical generalization of all essential features of such formulisms so that theorems applying to all could be proven once and for all. In this paper, (...) we extend Rieter's normal default theories, which have a number of the nice properties which make them a desirable context for belief revision, to the setting of nonmonotonic rule systems. Reiter defined a default theory to be normal if all the rules of the default theory satisfied a simple syntatic condition. However, this simple syntatic condition has no obvious analogue in the setting of nonmonotonic rule systems. Nevertheless, an analysis of the proofs of the main results on normal default theories reveals that the proofs do not rely on the particular syntactic form of the rules but rather on the fact that all rules have a certain consistency property. This led us to extend the notion of normal default theories with respect to a general consistency property. This extended notion of normal default theories, which we call Forward Chaining normal , is easily lifted to nonmonotomic rule systems and hence applies to general logic programs and truth maintenance. (shrink)

From electronic design problems to resolution proofs to SAT solvers, this book focuses on the satisfiabilityof theories that consist of propositional logic ...

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through (...) finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem. (shrink)

This breakthrough volume integrates European, British, and American scholarship in advanced areas of philosophy and decision theory. Contributions cover a broad area of economics--from criticism of institutional economics to examination of the role of induction in economic forecasting.

Michael A PetersBeijing Normal UniversityChatGPT is an AI chatbot released by OpenAI on November 30, 2022 and a ‘stable release’ on February 13, 2023. It belongs to OpenAI’s GPT-3 family (generativ...

Artykuł przedstawia polskie regulacje prawne z lat 1998-2007 będące podstawą lustracji. Analizuje szereg aktów prawnych prezentując zakładane cele lustracji, jej zakres, procedury i przewidywane sankcje karne. Celem autora jest identyfikacja aksjologicznych podstaw regulacji prawnych dotyczących lustracji. W trakcie analiz wskazuje on m. in. na brak proporcji między sankcjami karnymi a winą jednostek, zwłaszcza w niektórych przypadkach penalizacji oświadczeń lustracyjnych niezgodnych z prawdą lub penalizacji niezłożenia oświadczeń. Autor argumentuje także, że analizowane rozwiązania zakładały – wbrew deklarowanym celom – przeniesienie odpowiedzialności za (...) zło systemu politycznego z jego aktywnych twórców na jednostki wbrew woli poddane działaniu tego systemu. Ponadto argumentuje, że lustracja oparta na przeprowadzanym przez państwo „teście moralności” radykalnie ingeruje w wewnętrzną sferę moralności jednostki i stąd zakłada elementy typowe dla aksjologii systemów totalitarnych; państwo nakazuje dokonać działania, które bezpośrednio i wprost zmierza do realizacji ściśle wewnętrznej wartości moralnej opartej na zgodności oświadczenia z przekonaniami, i jednocześnie państwo ustanawia siebie nie tylko obserwatorem i sędzią realizacji tej wartości, ale także autorem wzorca przekonań, z którymi oświadczenie ma być zgodne. (shrink)

Works by Henryk Sienkiewicz, a Polish writer and the winner of the 1905 Nobel Prize for Literature, were subjected to verification by the DDR’s censorship apparatus several times. Censors considered his novellas which discussed 19th-century social issues as desirable and worth promoting among East German readers. His novel Krzyżacy, which was set in the Middle Ages, was accepted eagerly both by publishing houses and the censorship office as it enabled national socialism in Germany to be viewed in critical terms, as (...) the DDR distanced itself from the system. Reviewers did, however, find a major ideological threat for young readers in East Germany in a young adult novel entitled W pustyni i w puszczy, and for that reason it was withdrawn from the publishing procedure. (shrink)

The history of political transformation in Poland is an uninterrupted process of forming identifications along party lines, as well as of the political milieus’ searching, for a response to the question regarding the location of their own subjective space within the wider political sphere. It is worthwhile, when we discuss this, to ask whether the building up of a party’s identity is dictated by ideological and programmatic reasons or whether it is an incidental matter. The values and beliefs concealed in (...) the 80s, when the opposition belonged to the underground, have been permanently inscribed into the Polish political landscape. A group of doctrines which served as a component in the build-up of party identity may be perceived. The religious and national values, as well as the historical and cultural issues, which emerged into the daylight, may be treated as the embryo of certain ideas, which in time, as a result of public debates, have become fundamental determinants of many political parties. (shrink)