Adapting a claim of Kracht (Theor Comput Sci 354:131–141, 2006), we establish a characterization of the typable partial applicative structures.

Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.

This paper elaborates on the following correspondence theorem (which has been defended and formally proved elsewhere): if theory T has been empirically successful in a domain of applications A, but was superseded later on by a different theory T* which was likewise successful in A, then under natural conditions T contains theoretical expressions which were responsible for T’s success and correspond (in A) to certain theoretical expressions of T*. I illustrate this theorem at hand of the phlogiston versus oxygen theories (...) of combustion, and the classical versus relativistic theories of mass. The ontological consequences of the theorem are worked out in terms of the indirect reference and partial truth. The final section explains how the correspondence theorem may justify a weak version of scientific realism without presupposing the no-miracles argument. (shrink)

In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way (...) of formalizing Keynes' theory of economic action. (shrink)

Image restoration is a research hotspot in computer vision and computer graphics. It uses the effective information in the image to fill in the information of the designated damaged area. This has high application value in environmental design, film and television special effects production, old photo restoration, and removal of text or obstacles in images. In traditional sparse representation image restoration algorithms, the size of dictionary atoms is often fixed. When repairing the texture area, the dictionary atom will be too (...) large to cause blurring. When repairing a smooth area, the dictionary atom is too small to cause the extension of the area, which affects the image repair effect. In this paper, the structural sparsity of the block to be repaired is used to adjust the repair priority. By analyzing the structure information of the repair block located in different regions such as texture, edge, and smoothing, the size of the dictionary atom is adaptively determined. This paper proposes a color image restoration method that adaptively determines the size of dictionary atoms and discusses a model based on the partial differential equation restoration method. Through simulation experiments combined with subjective and objective standards, the repair results are evaluated and analyzed. The simulation results show that the algorithm can effectively overcome the shortcomings of blurred details and region extension in fixed dictionary restoration, and the restoration effect has been significantly improved. Compared with the results of several other classic algorithms, it shows the effectiveness of the algorithm in this paper. (shrink)

The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a (...) novel generalization of the idea of a field on spacetime, as well as a novel method of approximating the solutions to partial-differential equations on relativistic spacetimes in a way that tries to account for the peculiar needs of the interface between the exact structures of mathematical physics and the inexact data of experimental physics in a relativistically invariant way. It is argued, on the basis of these constructions, that the idea of a regime of propriety plays a central role in attempts to understand the semantical relations between theoretical and experimental knowledge of the physical world in general, and in particular in attempts to explain what it may mean to claim that a physical theory models or represents a kind of physical system. This discussion necessitates an examination of the initial-value formulation of the partial-differential equations of mathematical physics, which suggests a natural set of conditions---by no means meant to be canonical or exhaustive---one may require a mathematical structure, in conjunction with a set of physical postulates, satisfy in order to count as a physical theory. Based on the novel approximating methods developed for solving partial-differential equations on a relativistic spacetime by finite-difference methods, a technical result concerning a peculiar form of theoretical under-determination is proved, along with a technical result purporting to demonstrate a necessary condition for the self-consistency of a physical theory. (shrink)

In this dissertation we explore projective Fraïssé theory and its applications, as well as limitations, to the study of compact metrizable spaces. The goal of projective Fraïssé theory is to approximate spaces via classes of finite structures and glean topological or dynamical properties of a space by relating them to combinatorial features of the associated class of structures. Using the framework of compact metrixable structures, we establish general results which expand and help contextualize previous works in the (...) field. Many proofs in the domain of projective Fraïssé theory are carried out in a context dependent fashion and have thus far eluded clean generalizations. A reason is to be found in the lack of a clear understanding of which spaces are amenable to be studied via projective Fraïssé limits. We give both positive and negative results in this direction. We isolate a combinatorial condition which entails a correspondence between finite structures and regular quasi-partitions of compact metrizable spaces. This correspondence greatly aids the combinatorial-toplogical translation. We apply this machinery to study a class of one-dimensional compact metrizable spaces, which we call smooth fences. To this end, we isolate a class of finite structures—finite partial orders whose Hasse diagram is a forest—whose projective Fraïssé limit approximates a distinctive smooth fence with remarkable properties. We call it the Fraïssé fence and characterize it topologically by carefully exploiting the bridge between the combinatorial and topological worlds. We explore homogeneity and universality features of the Fraïssé fence and the properties of its spaces and endpoints, and provide some results on the dynamics of its group of homeomorphisms. The dissertation is partially based on [1, 2]. (shrink)

This paper uses a partially ordered set of syntactic categories to accommodate optionality and licensing in natural language syntax. A complex but well-studied data set pertaining to the syntax of quantifier scope and negative polarity licensing in Hungarian is used to illustrate the proposal. The presentation is geared towards both linguists and logicians. The paper highlights that the main ideas can be implemented in different grammar formalisms, and discusses in detail an implementation where the partial ordering on categories is (...) given by the derivability relation of a calculus with residuated and Galois-connected unary operators. (shrink)

The technical contribution of this paper is threefold.First we show how to encode functionals in a ‘flat’ applicative structure by adding oracles to untyped λ-calculus and mimicking the applicative behaviour of the functionals with an impredicatively defined reduction relation. The main achievement here is a Church-Rosser result for the extended reduction relation.Second, by combining the previous result with the model construction based on partial equivalence relations, we show how to extend a λ-closed simple type structure to a (...) model of the polymorphic λ-calculus.Third, we specialize the previous result to a counter model against a simple minimization. This minimization is realized by a bar recursive functional, which contrasts the results of Spector and Girard which imply that the bar recursive functions are exactly those that are definable in the polymorphic λ-calculus. As a spin-off, we obtain directly the non-conservativity of the extensions of Gödel's T with bar recursion, fan functional, and Luckhardt's minimization functional, respectively. For the latter two extensions these results are new. (shrink)

We employ the notions of "sequential function" and "interrogation" (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using Longley's preorder-enriched category of partial combinatory algebras and decidable applicative structures. We also investigate total combinatory algebras of partial functions. One of the results is that every realizability topos is a geometric quotient of a realizability topos on a total combinatory algebra.

In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many-sorted metric partial algebra, thus extending the axiomatisation given by Pour-El and Richards in [9] for Banach spaces. We show that every Banach-Mazur computable partial function from an effectively separable computable metric partial Σ-algebra A to a computable metric partial Σ-algebra B must be continuous, and conversely, that every effectively continuous partial function with semidecidable domain (...) and which preserves the computability of a computably enumerable dense set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour-El and Richards. (shrink)

In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many‐sorted metric partial algebra, thus extending the axiomatisation given by Pour‐El and Richards in [9] for Banach spaces. We show that every Banach‐Mazur computable partial function from an effectively separable computable metric partial Σ‐algebraAto a computable metric partial Σ‐algebraBmust be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves the (...) computability of a computably enumerable dense set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour‐El and Richards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

Most of us believe that partiality applies in a broad range of relationships. One relationship on which there is much disagreement is co-nationality. Some writers argue that co-national partiality is not justified in certain cases, like killing in war, since killing in defense of co-nationals is intuitively impermissible in other contexts. I argue that this approach overlooks an important structural feature of partiality—namely, that its scope is sometimes restricted. In this essay, I show how some relationships that generate reasons of (...) partiality are restricted in scope—that is, they generate reasons within particular contexts or with respect to particular goods. I then argue that co-national partiality is scope restricted. I then show how this fact helps proponents of co-national partiality overcome the aforementioned objection to its application in cases like war. (shrink)

Following Henkin's discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or "cardinality" quantifiers, e.g., "most", "few", "finitely many", "exactly α", where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general (...) definition of monotone-increasing (M↑) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwise's 1979 analysis of the basic case of M↑ POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional Ist-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages. (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. (...) Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. (...) Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

Following Henkin’s discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or “cardinality” quantifiers, e.g., “most”, “few”, “finitely many”, “exactly α ”, where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a (...) general definition of monotone-increasing (M↑) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwise’s 1979 analysis of the basic case of M↑ POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages. (shrink)

We study the structure of analytic ideals of subsets of the natural numbers. For example, we prove that for an analytic ideal I, either the ideal {X (Ω × Ω: En X ({0, 1,…,n} × Ω } is Rudin-Keisler below I, or I is very simply induced by a lower semicontinuous submeasure. Also, we show that the class of ideals induced in this manner by lsc submeasures coincides with Polishable ideals as well as analytic P-ideals. We study this class of (...) ideals and characterize, for example, when the ideals in it are Fσ or when they carry a locally compact group topology. We apply these results to Borel partial orders to rederive a theorem of Todorcevic and to Borel equivalence relations to answer a question of Kechris and Louveau. As another application we give a characterization of σ-ideals of μ-zero sets for Maharam submeasures μ on the Cantor set which is to a large extent analogous to a characterization of the meager ideal due to Kechris and the author. (shrink)

Various forms of mathematical induction are applicable to domains with some kinds of order. This naturally leads to the questions about the possibility of unification of different inductions and their generalization to wider classes of ordered domains. In the paper we propose a common framework for formulating induction proof principles in various structures and apply it to partially ordered sets. In this framework we propose a fixed induction principle which is indirectly applicable to the class of all posets. In (...) a certain sense, this result provides a solution to the problem of formulating a common generalization of a number of well-known induction principles for discrete and continuous ordered structures. (shrink)

It has become essential to create and apply new media in visual communication design due to social media existence. This study aims to investigate the role of innovative applications of new media in visual communication design in educational institutions. Traditional media design in visual communication lacks to disseminate information more effectively, which requires innovative change. Therefore, this study attempts to highlight the role of innovative application of new media in visual communication by considering visual expression design with information technology, flexible (...) layout, diversified modes of transmission, and interactivity of integration. For this purpose, this study adopted a quantitative research approach in which a cross-sectional research design is followed. A questionnaire survey is carried out to collect data from educational institutions in China. Partial Least Square-Structural Equation Modeling is used for data analysis. Results of the study indicated that innovative applications of new media have central importance in visual communication. However, resistance to innovative change has a negative role in the relationship between innovative applications of new media and visual communication design. Results of the study highlighted that visual expression design with IT, flexible layout, diversified modes of transmission, and interactivity of integration have a positive effect on visual communication design. Therefore, among the educational intuitions of China, implementing innovative applications related to the new media can lead to visual communication design. The results of this study provided several insights for the practitioners to promote communication methods among educational institutions. (shrink)

The technique of covers is now well established in semigroup theory. The idea is, given a semigroup S, to find a semigroup having a better understood structure than that of S, and an onto morphism of a specific kind from to S. With the right conditions on , the behaviour of S is closely linked to that of . If S is finite one aims to choose a finite . The celebrated results for inverse semigroups of McAlister in the 1970s (...) form the flagship of this theory.Weakly left quasi-ample semigroups form a quasivariety (of algebras of type(2, 1)), properly containing the classes of groups, and of inverse, left ample, and weakly left ample semigroups. We show how the existence of finite proper covers for semigroups in this quasivariety is a consequence of Ashs powerful theorem for pointlike sets. Our approach is to obtain a cover of a weakly left quasi-ample semigroup S as a subalgebra of S × G, where G is a group. It follows immediately from the fact that weakly left quasi-ample semigroups form a quasivariety, that is weakly left quasi-ample. We can then specialise our covering results to the quasivarieties of weakly left ample, and left ample semigroups. The latter have natural representations as (2, 1)-subalgebras of partial (one-one) transformations, where the unary operation takes a transformation to the identity map in the domain of . In the final part of this paper we consider representations of weakly left quasi-ample semigroups. (shrink)

The notion of a bilattice was rst introduced by Ginsburg (see Gin]) as a general framework for a diversity of applications (such as truth maintenance systems, default inferences and others). The notion was further investigated and applied for various purposes by Fitting (see Fi1]- Fi6]). The main idea behind bilattices is to use structures in which there are two (partial) order relations, having di erent interpretations. The two relations should, of course, be connected somehow in order for the (...) mathematical structure to be useful. It is not clear, however, what this connection should be. Ginsberg, for example, has made the connection through an extra operation of negation. Fitting, on the other hand, has investigated connections in the form of conditions on the structure (such as being interlaced { see below). These conditions are independent of the existence, or even the possibility to de ne, operations like Ginsberg's negation.* Fitting de nes, accordingly, notions like \an interlaced bilattice", \a distributive bilattice", \a bilattice with negation" and others. He does not provide, however, any de nition of the notion of bilattice itself (without an extra modi er). I was unable to nd anywhere, in fact, a de nition which will cover all the structures which were called \bilattice" in the literature. (shrink)

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, (...) which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation). (shrink)

In this article I revise and defend a core feature of political liberalism, namely, the idea that principles of political justice should be limited in their scope of application to what John Rawls calls the ‘basic structure of society.’ I refer to this feature as the ‘basic structure restriction’ of political liberalism. According to my account of the basic structure restriction, the basic structure includes all and only those institutions that have a profound effect on the lives of all citizens, (...) and thus those institutions that citizens would want to organize as parts of a fair system of social cooperation. Moreover, maintaining the basic structure as a fair system of social cooperation vis-à-vis all citizens requires the exercise of coercive political power. This account of the basic structure, which I call the ‘legitimacy of coercion account,’ shows that limiting the basic structure to those institutions that are maintained by legally coercive means is not arbitrary, contrary to the claims of critics like G. A. Cohen. Furthermore, by recognizing explicitly that there exist certain institutions – and, in particular, the family – that ought to be regulated partially by coercively maintained principles, my formulation of the basic structure provides a more satisfactory account of the way in which principles of justice should apply to the family than does Rawls’s most considered account. Finally, I explain how my account of the basic structure can incorporate many of S. M. Okin’s proposed policies for promoting gender equality in society. (shrink)

Purpose of the article is to present in two parts the selected aspects of application of monetary policy in the euro area pre and post 2008 as well as insitutional adaptations brought by the EU legislator. Methodology/methods In order to better explain these points, the article relies partially on a comparison with the framework and application of the monetary policy by the Federal Reserve as well as on a historic method when outlining the influence of definition of financial stability from (...) the ECB/eurosystem towards other prominent central banks. Scientific aim The article presents selected aspects of the monetary policy in the part of the EU where single currency was introduced in order to outline state of the art governance structure as well as a certain institutional creativity in application of powers conferred upon the central banks by the Treaty on the Functioning of the European Union and Protocol on the Statute of the European System of Central Banks and of the European Central Bank. The goal is to prove the hypothesis of robustness of the framework and present the limits that can only be pushed further by the legislative power. The conclusions confirm on the one hand that the framework of monetary policy based on strong institutional safeguards such as legislative power and independence is very resilient and can prove efficient and creative enough to stabilise an innovative monetary system, however, on the other hand, validate the hypothesis that certain adaptations can only be performed on the basis of a legislative adaptations. (shrink)

Purpose of the article is to present in two parts the selected aspects of application of monetary policy in the euro area pre and post 2008 as well as insitutional adaptations brought by the EU legislator. Methodology/methods In order to better explain these points, the article relies partially on a comparison with the framework and application of the monetary policy by the Federal Reserve as well as on a historic method when outlining the influence of definition of financial stability from (...) the ECB/eurosystem towards other prominent central banks. Scientific aim The article presents selected aspects of the monetary policy in the part of the EU where single currency was introduced in order to outline state of the art governance structure as well as a certain institutional creativity in application of powers conferred upon the central banks by the Treaty on the Functioning of the European Union and Protocol on the Statute of the European System of Central Banks and of the European Central Bank. The goal is to prove the hypothesis of robustness of the framework and present the limits that can only be pushed further by the legislative power. The conclusions confirm on the one hand that the framework of monetary policy based on strong institutional safeguards such as legislative power and independence is very resilient and can prove efficient and creative enough to stabilise an innovative monetary system, however, on the other hand, validate the hypothesis that certain adaptations can only be performed on the basis of a legislative adaptations. (shrink)

The application of artificial intelligence technology has evolved into an influential endeavor to improve firm performance, but little research considers the relationship among artificial intelligence capability, management, driven decision making, and firm performance. Based on the resource-based view and existing findings, this paper constructs a higher-order model of AIC and suggests a research model of e-commerce firm AIC and firm performance. We collected 394 valid questionnaires and conducted data analysis using partial least squares structural equation modeling. As a second-order (...) variable, AIC was formed by three first-order variables: basic, proclivity, and skills. AIC indirectly affects firm performance through creativity, AIM, and AI-driven decision making. Firm creativity, AIM, and AIDDM are essential variables between AIC and firm performance. Innovation culture positive moderates the relationship between firm creativity and AIDDM as well as the relationship between AIDDM and firm performance. Environmental dynamism positive mediates the connection between AIM and AIDDM. Among the control variables, firm age negatively affects firm performance, and employee size does not. This study helps enterprises leverage AI to improve firm performance, achieve a competitive advantage, and contribute to theory and management practice. (shrink)

In contemporary democracies, global capitalism exerts a significant influence over how state power is exercised, raising questions about where political power resides in global politics. This question is important, since our specific considerations about justifiability of political power, i.e. political legitimacy, depend on how we characterize political power at the global level. As a partial answer to this question, I argue that our notion of global political legitimacy should be reoriented to include the structural power of the Transnational Capitalist (...) Class as its subject matter. Structural power is a social relation in which the institutional context makes some agents comply with others’ preferences regardless of actors’ intentional efforts to bring about such outcomes. Even when global business elites do not intentionally exercise power to obtain political control of global governance, their structural power has recognizable effects that partly enforce the world order. To advance my claim, I utilize the radical realists’ argument that the notion of legitimacy is applicable to a broader range of social practices that are beyond dyadic power relations, i.e. rulers intentionally exercising power over subjects. (shrink)

We prove that if f is a partial Borel function from one Polish space to another, then either f can be decomposed into countably many partial continuous functions, or else f contains the countable infinite power of a bijection that maps a convergent sequence together with its limit onto a discrete space. This is a generalization of a dichotomy discovered by Solecki for Baire class 1 functions. As an application, we provide a characterization of functions which are countable (...) unions of continuous functions with domains of type Πn0, for a fixed n<ω. For Baire class 1 functions, this generalizes analogous characterizations proved by Jayne and Rogers for n=1 and Semmes for n=2. (shrink)

This paper develops an account of how economic and political institutions can limit the applicability of principles of justice even in non-relational cosmopolitan conceptions. It shows that fundamental principles of justice underdetermine fair distributive shares as well as justice -based requirements. It argues that institutions partially constitute the content of justice by determining distributive shares and by resolving indeterminacies about justice -based requirements resulting from strategic interaction and disagreement. In the absence of existing institutions principles of justice might not be (...) applicable for assessing distributions or guiding individual action and institutional design. Hence, accepting a specific cosmopolitan conception of justice is insufficient to settle global distributive questions. (shrink)

We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques-thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite (...) conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF. (shrink)

John Dewey, one of the most important thinkers of pragmatism, elaborated a specific conception of law partially and gradually in the long course of his intellectual career. This part of his broader philosophical outlook is analyzed here through one of its most important segments - application of law - and interpreted in its historical, social and cultural background. The first part of the article concentrates on the 'objective' reasons for giving emphasis to the application of law in his legal philosophy. (...) This domination of the application of law in his legal thought is derived from the needs of a rapidly changing structure of the American society in the first half of the XX century, and theoretically has its place in an all around phenomenon in American intellectual history in general that Morton White terms antiformalism. The second part of the article analyses his legal conceptions and their connection with the general philosophical position of this pragmatist. Dewey formed his conception of application of law as an integral part of his broader philosophical standpoint, and especially on the basis of his radical reinterpretation of logic and truth. Since his understanding of the legal process has roots in his experimentalist conception of logic that encompasses the apprehension of the process of experimentation as the only warrant for the validity of propositions, he regards application as conditio sine qua non of the legality of norms in general. This leads us to the last part of the article that scathes possible lines of critical approach to Dewey's work in this field. The view that the legality of norms is derived from their application is in legal theory often regarded as sociologism, inasmuch as it disregards the normative aspects of the legal process and emphasizes the social ones to the point of making it void of the normative aspects in the totality of the process itself. The proper understanding of possible lines of criticism of Dewey's standpoints in legal philosophy guides us back again to confront his conceptions with their cultural background, with which the article begins. Autor se u clanku bavi koncepcijom primjene prava u filozofiji Dzona Djuija, pragmatiste bez presedana u obuhvatnosti i temeljnosti bavljenja filozofskim problemima, cije je misljenje na ovim prostorima rijetko bilo predmet razmatranja. Zamisljen kao uvodno ispitivanje filozofsko-pravne problematike u Djuijevoj filozofiji, clanak u prvom dijelu razmatra odnos njegove filozofije prava i americkog kulturnog konteksta. U drugom dijelu je izlozeno Djuijevo shvatanje primjene prava i konfrontirano je s njegovim opstim filozofskim tezama, u prvom redu s koncepcijom logike kao 'ispitivanja ispitivanja'. Konacno, autor pokusava da ocrta osnovne smjernice kritickog pristupa Djuijevim rjesenjima filozofsko-pravnih problema. (shrink)

The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). The (...) simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only. The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function. (shrink)

The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of P, (...) where in general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of P. ;In classical propositional logic, propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies . However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying , and can be provided. ;Von Neumann first proposed that the algebraic structures of the subspaces of Hilbert space be regarded as the propositional structures P of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible and incompatible ; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality ,) applicable to the Plattices; and truth-functionality ) applicable to both the Plattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional ,) semantics for any PQM lattice containing incompatible elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional ) semantics for three-or-higher dimensional Hilbert space PQM structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. ;The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is bivalent, i.e., the value 1 or 0 is assigned to each proposition, and truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. (shrink)

W. D. Ross’s ethical theory requires us somehow to compare the metaphorical “weights” of different prima facie duties, but it leaves mysterious how this might be done. The formulation of a procedure to achieve such a comparison would be desirable on practical, theoretical, and pedagogical grounds. I formulate a procedure that is congenial to Ross’s theory. Central to my procedure are instructions to characterize the weight of each prima facie duty with respect to (a) the general stringency of this kind (...) of duty, (b) the stringency of this particular duty relative to other duties of its own kind, and (c) the degree to which the duty specifically demands the particular action that it favors in a given case. The procedure leads to a determination of one’s actual, all-things-considered duty in some cases but not in all. (shrink)

W. D. Ross’s ethical theory requires us somehow to compare the metaphorical “weights” of different prima facie duties, but it leaves mysterious how this might be done. The formulation of a procedure to achieve such a comparison would be desirable on practical, theoretical, and pedagogical grounds. I formulate a procedure that is congenial to Ross’s theory. Central to my procedure are instructions to characterize the weight of each prima facie duty with respect to (a) the general stringency of this kind (...) of duty, (b) the stringency of this particular duty relative to other duties of its own kind, and (c) the degree to which the duty specifically demands the particular action that it favors in a given case. The procedure leads to a determination of one’s actual, all-things-considered duty in some cases but not in all. (shrink)

The thesis proposes, defends, and applies a new model of inter-theoretic reduction, called "Neo-Nagelian" reduction. There are numerous accounts of inter-theoretic reduction in the philosophy of science literature but the most well-known and widely-discussed is the Nagelian one. In the thesis I identify various kinds of problems which the Nagelian model faces. Whilst some of these can be resolved, pressing ones remain. In lieu of the Nagelian model, other models of inter-theoretic reduction have been proposed, chief amongst which are so-called (...) "New Wave" models. I show these to be no more adequate than the original Nagelian model. I propose a new model of inter-theoretic reduction, Neo-Nagelian reduction. This model is structurally similar to the Nagelian one, but differs in substantive ways. In particular I argue that it avoids the problems pertaining to both the Nagelian and New Wave models. Multiple realizability looms large in discussions about reduction: it is claimed that multiply realizable properties frustrate the reduction of one theory to another in various ways. I consider these arguments and show that they do not undermine the Neo-Nagelian of reduction of one theory to another. Finally, I apply the model to statistical mechanics. Statistical mechanics is taken to be a reductionist enterprise: one of the aims of statistical mechanics is to reduce thermodynamics. Without an adequate model of inter-theoretic reduction one cannot assess whether it succeeds; I use the Neo-Nagelian model to critically discuss whether it does. Specifically, I consider two very recent derivations of the Second Law of thermodynamics, one from Boltzmannian classical statistical mechanics and another from quantum statistical mechanics. I argue that they are partially successful, and that each makes for a promising line of future research. (shrink)

The question motivating my investigation is: Are the basic philosophical principles underlying the "core" system of contemporary logic exhausted by the standard version? In particular, is the accepted narrow construal of the notion "logical term" justified? ;As a point of comparison I refer to systems of 1st-order logic with generalized quantifiers developed by mathematicians and linguists . Based on an analysis of the Tarskian conception of the role of logic I show that the standard division of terms into logical and (...) extra-logical is partly arbitrary. I argue that the semantic principles of Tarskian logic allow any higher order mathematical predicate or relation to function as a logical term in a 1st-order system, provided it is introduced in the right way into the syntactic-semantic apparatus. ;Formally, I propose a new, "constructive", semantic characterization of logical terms. A logical term is defined by a function which, given a model, "shows" how to construct relations, sets, or n-tuples of individuals which satisfy it. I discuss the linguistic applicability of the extended logic and bring numerous examples. ;One chapter is devoted to branching quantification--a non-standard logico-linguistic construction obtained by affixing a non-linear, partially-ordered quantifier-prefix to a well-formed formula. Although standard branching quantifiers were given a complete account by Henkin and Walkoe, it is not altogether clear what the meaning of branching generalized quantifiers is. I propose a new analysis of the generalized branching prefix which extends the existent, partial, definitions due to Barwise, and I develop a generalization leading to a "family" of branching structures. ;In conclusion I discuss the philosophical impact of the generalized conception of logic on such issues as the logicist thesis, the interaction between mathematics and logic, ontological commitment via logic, metaphysics and logical semantics. (shrink)

People tend to rank values of all kinds linearly from good to bad, but there is little reason to think that this is reasonable or correct. This book argues, to the contrary, that values are often partially ordered and hence frequently incomparable. Proceeding logically from a small set of axioms, John Nolt examines the great variety of partially ordered value structures, exposing fallacies that arise from overlooking them. He reveals various ways in which incomparability is obscured: using linear indices (...) to summarize partially ordered data, relying on an inadequately defined concept of parity, or conflating incomparability with vagueness. Incomparability can enrich and clarify a range of topics including the paradoxes of Derek Parfit, rational decision theory, and the infinite values of theology. Finally, Nolt shows how to generalize many of the concepts introduced earlier, explores the intricate depths of certain noteworthy partially ordered value structures, and argues for the finitude of value. Incomparable Values will be of interest to scholars and advanced students working in ethics, value theory, rational decision theory, and logic. (shrink)

The problem of finding a covariant expression for the distribution and conservation of gravitational energy-momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann's realization that there are infinitely many gravitational energy-momenta. Initially use is made of a flat background metric (or rather, all of them) or connection, because the desired gauge invariance properties are obvious. Partial gauge-fixing then yields an appropriate covariant quantity without any background metric or connection; one version is the collection of (...) pseudotensors of a given type, such as the Einstein pseudotensor, in _every_ coordinate system. This solution to the gauge covariance problem is easily adapted to any pseudotensorial expression (Landau-Lifshitz, Goldberg, Papapetrou or the like) or to any tensorial expression built with a background metric or connection. Thus the specific functional form can be chosen on technical grounds such as relating to Noether's theorem and yielding expected values of conserved quantities in certain contexts and then rendered covariant using the procedure described here. The application to angular momentum localization is straightforward. Traditional objections to pseudotensors are based largely on the false assumption that there is only one gravitational energy rather than infinitely many. (shrink)

Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames.

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some (...) examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)

An infinitary characterisation of the first-order sentences true in all substructures of a structure M is used to obtain partial reduction of the decision problem for such sentences to that for Th(M). For the relational structure $\langle\mathbf{R}, \leq, +\rangle$ this gives a decision procedure for the ∃ x∀ y-part of the theory of all substructures, yet we show that the ∃ x 1x 2 ∀ y-part, and the entire theory, is Π 1 1 -complete. The theory of all ordered (...) subsemigroups of $\langle\mathbf{R}, \leq, +\rangle$ is also shown Π 1 1 -complete. Applications in the philosophy of science are mentioned. (shrink)

We develop the theory of partial satisfaction relations for structures that may be proper classes and define a satisfaction predicate ($\models^*$) appropriate to such structures. We indicate the utility of this theory as a framework for the development of the metatheory of first-order predicate logic and set theory, and we use it to prove that for any recursively enumerable extension $\Theta$ of ZF there is a finitely axiomatizable extension $\Theta'$ of GB that is a conservative extension of (...) $\Theta$. We also prove a conservative extension result that justifies the use of $\models^*$ to characterize ground models for forcing constructions. (shrink)

We formulate C. Freiling's axioms of symmetry for general second-order structures with respect to a certain ideal of small sets contained in them and find several equivalent formulations of the principles. Then we focus on particular models, namely saturated and recursively saturated ones, and show that they are symmetric with respect to appropriate classes of small sets when their second-order part consists of definable sets. Some asymmetric models are also exhibited as well as partial asymmetric ones constructed by (...) forcing. (shrink)

A number of results have been obtained concerning Borel structures starting with Silver and Friedman followed by Harrington, Shelah, Marker, and Louveau. Friedman also initiated the model theory of Borel (in fact totally Borel) structures. By this we mean the study of the class of Borel models of a given first-order theory. The subject was further investigated by Steinhorn. The present work is meant to go further in this direction. It is based on the assumption that the study (...) of the class of, say, countable models of a theory reduces to analyzing a single $\omega_1$-saturated model. The question then arises as to when such a model can be totally Borel. We present here a partial answer to this problem when the theory under investigation is superstable. (shrink)

We prove an Ax-Kochen-Ershov like transfer principle for groups acting on groups. The simplest case is the following: let B be a soluble group acting on an abelian group G so that G is a torsion-free divisible module over the group ring Z[B], then the theory of B determines the one of the two-sorted structure $\langle G, B, *\rangle$ , where * is the action of B on G. More generally, we show a similar principle for structures $\langle G, (...) B, *\rangle$ , where G is a torsion-free divisible module over the quotient of Z[B] by the annulator of G. Two applications come immediately from this result: First, for not necessarily commutative domains, where we consider the action of a subgroup of the invertible elements on the additive group. We obtain then the decidability of a weakened structure of ring, with partial multiplication. The second application is to pure groups. The semi-direct product of G by B is bi- interpretable with our structure $\langle G, B, *\rangle$ . Thus, we obtain stable decidable groups that are not linear over a field. (shrink)

Intellectual humility plays a crucial role among intellectual virtues. It has attracted considerable attention from virtue epistemologists, who have offered a fair number of treatments. In this essay, I argue that, regardless of the difference among these treatments, they are beset by two problems: they fall into a circular argument; they fall into a self-referential contradiction. I then argue that a recent proposal by D. Pritchard allows us to avoid, but not. However, by combining this proposal with another reflection advanced (...) by the same author while he discusses the Wittgensteinian notion of hinge commitments, it is possible to avoid. The thesis that emerges is that only a partial application of intellectual humility solves. Finally, I reinforce this thesis by rejecting an alternative solution to. (shrink)

In this paper, we investigate how certain types of predicates should be connected with certain types of degree scales, and how this can affect the events they describe. The distribution and interpretation of various degree adverbials will serve us as a guideline in this perspective. They suggest that two main types of degree scales should be distinguished: (i) quantity scales, which are characterized by the semantic equivalence of Yannig ate the cake partially and Yannig ate part of the cake; quantity (...) scales only appear with verbs possessing an incremental theme (cf. Dowty 1991); (ii) intensity scales, which are characterized by degree modifiers (e.g., extremely, perfectly) receiving an intensive interpretation; intensity scales typically occur with verbs morphologically related to an adjective (to dry). More generally, we capitalize on a typology of degree structures to explain how degrees play a central role with respect to event structure. (shrink)