Completeness in Equational Hybrid Propositional Type Theory

Studia Logica - Equational hybrid propositional type theory ( $$\mathsf {EHPTT}$$ ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to...     

Ethical Theory,Completeness &; Consistency

This paper argues that many leading ethical theories are incomplete, in that they fail to account for both right and wrong. It also argues that some leading ethical theories are inconsistent, in that they allow that an act can be both right and wrong. The paper also considers responses on behalf of the target theories.     

Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere

A hybrid logic is obtained by adding to an ordinary modal logic further expressive power in the form of a second sort of propositional symbols called nominals and by adding so-called satisfaction operators. In this paper we consider hybridized versions of S5 (“the logic of everywhere”) and the modal logic of inequality (“the logic of elsewhere”). We give natural deduction systems for the logics and we prove functional completeness results.     

Completeness and super-valuations

This paper uses the notion of Galois-connection to examine the relation between valuation-spaces and logics. Every valuation-space gives rise to a logic, and every logic gives rise to a valuation space, where the resulting pair of functions form a Galois-connection, and the composite functions are closure-operators. A valuation-space (resp., logic) is said to be complete precisely if it is Galois-closed. Two theorems are proven. A logic is complete if and only if it is reflexive and transitive. A valuation-space is complete if and only if it is closed under formation of super-valuations.     

Structural Completeness in Relevance Logics

It is proved that the relevance logic \({\mathbf{R}}\) (without sentential constants) has no structurally complete consistent axiomatic extension, except for classical propositional logic. In fact, no other such extension is even passively structurally complete.     

Completeness of quantum logic

This paper is based on a semantic foundation of quantum logic which makes use of dialog-games. In the first part of the paper the dialogic method is introduced and under the conditions of quantum mechanical measurements the rules of a dialog-game about quantum mechanical propositions are established. In the second part of the paper the quantum mechanical dialog-game is replaced by a calculus of quantum logic. As the main part of the paper we show that the calculus of quantum logic is complete and consistent with respect to the dialogic semantics. Since the dialog-game does not involve the excluded middle the calculus represents a calculus of effective (intuitionistic) quantum logic.In a forthcoming paper it is shown that this calculus is equivalent to a calculus of sequents and more interestingly to a calculus of propositions. With the addition of the excluded middle the latter calculus is a model for the lattice of subspaces of a Hilbert space.On leave of absence from the Institut für Theoretische Physik der Universität zu Köln, W.-Germany.     

Dynamic Topological Completeness for

Dynamic topological logic (DTL) combines topological and temporalmodalities to express asymptotic properties of dynamic systemson topological spaces. A dynamic topological model is a tripleX ,f , V , where X is a topological space, f : X X a continuousfunction and V a truth valuation assigning subsets of X to propositionalvariables. Valid formulas are those that are true in every model,independently of X or f. A natural problem that arises is toidentify the logics obtained on familiar spaces, such as . It [9] it was shown that any satisfiable formulacould be satisfied in some for n large enough, but the question of how the logic varieswith n remained open. In this paper we prove that any fragment of DTL that is completefor locally finite Kripke frames is complete for . This includes DTL; it also includes some largerfragments, such as DTL₁, where "henceforth" may not appear inthe scope of a topological operator. We show that satisfiabilityof any formula of our language in a locally finite Kripke frameimplies satisfiability in by constructing continuous, open maps from the plane intoarbitrary locally finite Kripke frames, which give us a typeof bisimulation. We also show that the results cannot be extendedto arbitrary formulas of DTL by exhibiting a formula which isvalid in but not in arbitrarytopological spaces.     

Psychologism and Completeness in the Arts

When is an artwork complete? Most hold that the correct answer to this question is psychological in nature. A work is said to be complete just in case the artist regards it as complete or is appropriately disposed to act as if he or she did. Even though this view seems strongly supported by metaphysical, epistemological, and normative considerations, this article argues that such psychologism about completeness is mistaken, fundamentally, because it cannot make sense of the artist's own perspective on his or her work. For the artist, the question is not about his or her own psychology, but about the character of the work and the context in which he or she works. A nonpsychological account of completeness, on which completeness is a question of whether the work satisfies the conditions implicit in the artist's plan, avoids this problem and is equally or better able to explain the metaphysical, epistemic, and normative phenomena which appeared to support psychologism.     

Asymptotic Densities in Logic and Type Theory

This paper presents a systematic approach for obtaining results from the area of quantitative investigations in logic and type theory. We investigate the proportion between tautologies (inhabited types) of a given length n against the number of all formulas (types) of length n. We investigate an asymptotic behavior of this fraction. Furthermore, we characterize the relation between number of premises of implicational formula (type) and the asymptotic probability of finding such formula among the all ones. We also deal with a distribution of these asymptotic probabilities. Using the same approach we also prove that the probability that randomly chosen fourth order type (or type of the order not greater than 4), which admits decidable lambda definability problem, is zero. Presented by Jacek Malinowski     

Husserl's Two Notions Of Completeness

In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures hegave in Göttingen in 1901 and other related texts of the same period,a problem that had occupied Husserl since the beginning of 1890, whenhe was planning a never published sequel to Philosophie der Arithmetik(1891). In order to solve the problem of imaginary entities Husserl introduced,independently of Hilbert, two notions of completeness (definiteness in Husserl'sterminology) for a formal axiomatic system. I present and discuss these notionshere, establishing also parallels between Husserl's and Hilbert's notions ofcompleteness.     

The Art Type Theory of Art

Abstract

The theory I present and defend in this paper—what I term the art type theory— holds that something is a work of art iff it belongs to an established art type. Something is an established art type, in turn, either because its paradigmatic instances standardly satisfy eight art-making conditions, or because the art world has seen fit to enfranchise it as such. It follows that the art status of certain objects is independent of what any individual or culture might say about it, while the art status of others fundamentally depends on the judgment of the art world. Because of the theory's quasi-institutional component, I conclude by defending it against four objections that have been raised against institutional definitions.