Some remarks on extending and interpreting theories with a partial predicate for truth

1986 ◽  
Vol 15 (2) ◽  
pp. 219-251 ◽  
Author(s):  
William N. Reinhardt
Keyword(s):  
Partial Predicate

scholarly journals Kleene Algebra of Partial Predicates

2018 ◽  
Vol 26 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Artur Korniłowicz ◽  
Ievgen Ivanov ◽  
Mykola Nikitchenko
Keyword(s):  
Fixed Point ◽  
Regular Expressions ◽  
Dynamical Models ◽  
Kleene Algebra ◽  
Partial Property ◽  
De Morgan Algebras ◽  
Partial Predicate ◽  
Linguistic Approaches ◽  
Partial Predicates ◽  
Truth Tables

Summary We show that the set of all partial predicates over a set D together with the disjunction, conjunction, and negation operations, defined in accordance with the truth tables of S.C. Kleene’s strong logic of indeterminacy [17], forms a Kleene algebra. A Kleene algebra is a De Morgan algebra [3] (also called quasi-Boolean algebra) which satisfies the condition x ∧¬:x ⩽ y ∨¬ :y (sometimes called the normality axiom). We use the formalization of De Morgan algebras from [8]. The term “Kleene algebra” was introduced by A. Monteiro and D. Brignole in [3]. A similar notion of a “normal i-lattice” had been previously studied by J.A. Kalman [16]. More details about the origin of this notion and its relation to other notions can be found in [24, 4, 1, 2]. It should be noted that there is a different widely known class of algebras, also called Kleene algebras [22, 6], which generalize the algebra of regular expressions, however, the term “Kleene algebra” used in this paper does not refer to them. Algebras of partial predicates naturally arise in computability theory in the study on partial recursive predicates. They were studied in connection with non-classical logics [17, 5, 18, 32, 29, 30]. A partial predicate also corresponds to the notion of a partial set [26] on a given domain, which represents a (partial) property which for any given element of this domain may hold, not hold, or neither hold nor not hold. The field of all partial sets on a given domain is an algebra with generalized operations of union, intersection, complement, and three constants (0, 1, n which is the fixed point of complement) which can be generalized to an equational class of algebras called DMF-algebras (De Morgan algebras with a single fixed point of involution) [25]. In [27] partial sets and DMF-algebras were considered as a basis for unification of set-theoretic and linguistic approaches to probability. Partial predicates over classes of mathematical models of data were used for formalizing semantics of computer programs in the composition-nominative approach to program formalization [31, 28, 33, 15], for formalizing extensions of the Floyd-Hoare logic [7, 9] which allow reasoning about properties of programs in the case of partial pre- and postconditions [23, 20, 19, 21], for formalizing dynamical models with partial behaviors in the context of the mathematical systems theory [11, 13, 14, 12, 10].

Parametric optimization of anisogrid shells of irregular structure

2019 ◽  
Author(s):  
T.V. Burnysheva ◽  
O.A. Shteynbrekher
Keyword(s):  
Optimal Design ◽  
Parametric Optimization ◽  
Feasible Region ◽  
Irregular Structure ◽  
Simplex Search ◽  
Simplex Search Method ◽  
Rib Structure ◽  
Partial Predicate ◽  
Mesh Structures ◽  
Research Show

The paper focuses on an approach to solving the problem of parametric optimization of anisogrid mesh shells with an irregular structure. Mesh structures are widely used in building and engineering. This study deals with the optimal design of such structures used in aerospace industry. The problem of optimal design of mesh structures is relevant, as it makes it possible to increase the efficiency of their use, minimizing the weight, provided the strength and stability conditions are met. In our work we formulate the problem of optimal design of mesh structures in general form, and introduce an optimization algorithm based on the simplex search method in which we use a partial predicate of a feasible region to describe the non-convex smooth areas of boundaries. The results of solving the optimization problem for a particular structure with a violation of the regularity of the rib structure are given. Findings of research show that the considered algorithm can be used for optimal design of both regular and non-regular mesh structures.

The Quest for Cognates: A Reconstruction of Oblique Subject Constructions in Proto-Indo-European

2013 ◽  
Vol 3 (1) ◽  
pp. 28-67 ◽  
Author(s):  
Jóhanna Barðdal ◽  
Thomas Smitherman
Keyword(s):  
Present Article ◽  
Argument Structure ◽  
Individual Development ◽  
Data Sets ◽  
Early Archaic ◽  
Dative Subject ◽  
Semantic Alignment ◽  
Competing Hypotheses ◽  
Partial Predicate ◽  
Object Status

The enigma of the origin of non-canonical subject marking in the world’s languages has been met with two competing hypotheses: the Object-to-Subject Hypothesis and the Oblique Subject/Semantic Alignment Hypothesis (cf. Eythórsson and Barðdal, 2005). The present article argues in favor of the Oblique Subject/Semantic Alignment Hypothesis, presenting five sets of cognate predicates in the early/archaic Indo-European daughter languages that occur in the Oblique Subject Construction. These cognate sets have not figured in the earlier literature. Not only are they stem cognates, but they also occur in a cognate compositional predicate and argument structure construction, with a dative subject, the verb ‘be’ and an adjective, a noun, or an adverb. The discovery of these cognate data sets immediately invalidates the axiomatic assumption that non-canonical subject marking must originate in an earlier object status of these arguments. The data, moreover, form the input of a correspondence set, on which basis we reconstruct predicate-specific oblique subject constructions, a partial predicate-specific oblique subject construction, as well as a more abstract schematic dative subject construction for Proto-Indo-European, using the formalism of Sign-based Construction Grammar. The evidence presented here thus suggests that oblique subjects are inherited from an early proto-stage and do not represent an individual development in the Indo-European daughter languages.

Planning with abstraction based on partial predicate mappings

1994 ◽  
Vol 12 (4) ◽  
pp. 409-437
Author(s):  
Yoshiaki Okubo ◽  
Makoto Haraguchi
Keyword(s):  
Partial Predicate
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