Search results for " Completeness"
showing 10 items of 16 documents
Lambda substitution algebras
1993
In the paper an algebraic metatheory of type-free λ-calculus is developed. Our version is based on lambda substitution algebras (λSAs), which are just SAs introduced by Feldman (for algebraizing equational logic) enriched with a countable family of unary operations of λ-abstraction and a binary operation of application. Two representation theorems, syntactical and semantic, are proved, what directly provides completeness theorems.
Unification in first-order transitive modal logic
2019
We introduce unification in first-order transitive modal logics, i.e. logics extending Q–K4, and apply it to solve some problems such as admissibility of rules. Unifiable formulas in some extensions of Q–K4 are characterized and an explicit basis for the passive rules (those with non-unifiable premises) is provided. Both unifiability and passive rules depend on the number of logical constants in the logic; we focus on extensions of Q–K4 with at most four constants ⊤,⊥,□⊥,◊⊤. Projective formulas, defined in a way similar to propositional logic, are used to solve some questions concerning the disjunction and existence properties. A partial characterization of first-order modal logics with pr…
Completeness and timeliness: Cancer registries could/should improve their performance.
2015
Abstract Cancer registries must provide complete and reliable incidence information with the shortest possible delay for use in studies such as comparability, clustering, cancer in the elderly and adequacy of cancer surveillance. Methods of varying complexity are available to registries for monitoring completeness and timeliness. We wished to know which methods are currently in use among cancer registries, and to compare the results of our findings to those of a survey carried out in 2006. Methods In the framework of the EUROCOURSE project, and to prepare cancer registries for participation in the ERA-net scheme, we launched a survey on the methods used to assess completeness, and also on t…
Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces
2012
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004…
Scattering theory for a class of fermionic Pauli–Fierz models
2004
Abstract The scattering theory for a class of fermionic Pauli–Fierz models is considered. We give a proof of the asymptotic completeness of the dynamics in the case of massive fermions. The result applied to the Hamiltonian of a quantized spin- 1 2 Dirac particle interacting with an external field through a cutoff Yukawa interaction and to the Hamiltonian of a system of finitely many confined particles coupled to a fermionic field with a quadratic interaction.
Performability of Actions
2021
AbstractAction theory may be regarded as a theoretical foundation of AI, because it provides in a logically coherent way the principles of performing actions by agents. But, more importantly, action theory offers a formal ontology mainly based on set-theoretic constructs. This ontology isolates various types of actions as structured entities: atomic, sequential, compound, ordered, situational actions etc., and it is a solid and non-removable foundation of any rational activity. The paper is mainly concerned with a bunch of issues centered around the notion of performability of actions. It seems that the problem of performability of actions, though of basic importance for purely practical ap…
Realism, metamathematics, and the unpublished essays
1995
This initial chapter is divided into two sections. The first is devoted to a brief exposition of the intuitive essence and the philosophical motivation of Godel’s main metamathematical results, namely his completeness theorem for elementary logic (1930) and his incompleteness theorems for arithmetic (1931). Thereafter some discussion of the different ways to confront the relationship between those results and Godel’s philosophical realism in logic and mathematics is offered. Thus, mathematical realism will be successively regarded as (i) a philosophical consequence of those results; (ii) a heuristic principle which leads to them; (iii) a philosophical hypothesis which is “verified” by them.…
Protoalgebraicity and the Deduction Theorem
2001
This chapter is intended as an introduction to the Deduction Theorem and to applications of this theorem in metalogic.
Scattering resonances and Pseudospectrum : stability and completeness aspects in optical and gravitational systems
2022
The general context of this thesis is an effort to establish a bridge between gravitational andoptical physics, specifically in the context of scattering problems using as a guideline concepts andtools taken from the theory of non-self-adjoint operators. Our focus is on Quasi-Normal Modes(QNMs), namely the natural resonant modes of open leaky structures under linear perturbationssubject to outgoing boundary conditions. They also are referred to as scattering resonances.In the conservative self-adjoint case the spectral theorem guarantees the completeness andspectral stability of the associated normal modes. In this sense, a natural question in the non-self-adjoint setting refers to the char…
Deontology of Compound Actions
2018
This paper, being a companion to the book [2] elaborates the deontology of sequential and compound actions based on relational models and formal constructs borrowed from formal linguistics. The semantic constructions presented in this paper emulate to some extent the content of [3] but are more involved. Although the present work should be regarded as a sequel of [3] it is self-contained and may be read independently. The issue of permission and obligation of actions is presented in the form of a logical system . This system is semantically defined by providing its intended models in which the role of actions of various types (atomic, sequential and compound ones) is accentuated. Since the…