A First-Order Language for Expressing Aliasing and Type Properties of Logic Programs

1998 ◽  
pp. 184-199 ◽  
Author(s):  
Paolo Volpe
Keyword(s):  
Logic Programs ◽  
First Order ◽  
Order Language

Topological Model Set Deformations in Logic Programming

1989 ◽  
Vol 12 (3) ◽  
pp. 357-399
Author(s):  
Aida Batarekh ◽  
V.S. Subrahmanian
Keyword(s):  
Logic Programming ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Logic Programs ◽  
First Order ◽  
Order Language ◽  
Language L ◽  
General Logic ◽  
Model Set ◽  
Necessary And Sufficient

Given a first order language L, and a notion of a logic L w.r.t. L, we investigate the topological properties of the space of L-structures for L. We show that under a topology called the query topology which arises naturally in logic programming, the space of L-models (where L is a decent logic) of any sentence (set of clauses) in L may be regarded as a (closed, compact) T4-space. We then investigate the properties of maps from structures to structures. Our results allow us to apply various well-known results on the fixed-points of operators on topological spaces to the semantics of logic programming – in particular, we are able to derive necessary and sufficient topological conditions for the completion of covered general logic programs to be consistent. Moreover, we derive sufficient conditions guaranteeing the consistency of program completions, and for logic programs to be determinate. We also apply our results to characterize consistency of the unions of program completions.

scholarly journals Decidability of the Clark's completion semantics for monadic programs and queries

2014 ◽  
Vol 15 (3) ◽  
pp. 402-412
Author(s):  
LEVON HAYKAZYAN
Keyword(s):  
Logic Programming ◽  
Logic Programs ◽  
First Order ◽  
Order Language ◽  
General Logic ◽  
Turing Complete

AbstractThere are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable. To obtain decidability one needs to put additional restrictions on programs and queries. In logic programming it is natural to put restrictions on the underlying first-order language. In this note, we show the decidability of the Clark's completion semantics for monadic general programs and queries.

Weakly atomic-compact relational structures

1971 ◽  
Vol 36 (1) ◽  
pp. 129-140 ◽  
Author(s):  
G. Fuhrken ◽  
W. Taylor
Keyword(s):  
Abelian Group ◽  
Model Theory ◽  
Compact Abelian Group ◽  
Finite Subset ◽  
Relational Structure ◽  
Similarity Type ◽  
First Order ◽  
Relational Structures ◽  
Order Language ◽  
Weakly Atomic

A relational structure is called weakly atomic-compact if and only if every set Σ of atomic formulas (taken from the first-order language of the similarity type of augmented by a possibly uncountable set of additional variables as “unknowns”) is satisfiable in whenever every finite subset of Σ is so satisfiable. This notion (as well as some related ones which will be mentioned in §4) was introduced by J. Mycielski as a generalization to model theory of I. Kaplansky's notion of an algebraically compact Abelian group (cf. [5], [7], [1], [8]).

scholarly journals ON PRODUCTS OF ELEMENTARILY INDIVISIBLE STRUCTURES

2016 ◽  
Vol 81 (3) ◽  
pp. 951-971
Author(s):  
NADAV MEIR
Keyword(s):  
New Products ◽  
Elementary Substructure ◽  
First Order ◽  
Order Language ◽  
Image Position

AbstractWe say a structure ${\cal M}$ in a first-order language ${\cal L}$ is indivisible if for every coloring of its universe in two colors, there is a monochromatic substructure ${\cal M}\prime \subseteq {\cal M}$ such that ${\cal M}\prime \cong {\cal M}$. Additionally, we say that ${\cal M}$ is symmetrically indivisible if ${\cal M}\prime$ can be chosen to be symmetrically embedded in ${\cal M}$ (that is, every automorphism of ${\cal M}\prime$ can be extended to an automorphism of ${\cal M}$). Similarly, we say that ${\cal M}$ is elementarily indivisible if ${\cal M}\prime$ can be chosen to be an elementary substructure. We define new products of structures in a relational language. We use these products to give recipes for construction of elementarily indivisible structures which are not transitive and elementarily indivisible structures which are not symmetrically indivisible, answering two questions presented by A. Hasson, M. Kojman, and A. Onshuus.

scholarly journals Word order in Latin locative constructions: a corpus study in Caesar’s De bello gallico

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Stavros Skopeteas
Keyword(s):  
Word Order ◽  
Information Structure ◽  
Motion Verbs ◽  
Structural Domains ◽  
Corpus Study ◽  
First Order ◽  
Order Language ◽  
Free Word

AbstractClassical Latin is a free word order language, i.e., the order of the constituents is determined by information structure rather than by syntactic rules. This article presents a corpus study on the word order of locative constructions and shows that the choice between a Theme-first and a Locative-first order is influenced by the discourse status of the referents. Furthermore, the corpus findings reveal a striking impact of the syntactic construction: complements of motion verbs do not have the same ordering preferences with complements of static verbs and adjuncts. This finding supports the view that the influence of discourse status on word order is indirect, i.e., it is mediated by information structural domains.

On Axiomatizability of Non-Commutative Lp-Spaces

2007 ◽  
Vol 50 (4) ◽  
pp. 519-534
Author(s):  
C. Ward Henson ◽  
Yves Raynaud ◽  
Andrew Rizzo
Keyword(s):  
Hilbert Spaces ◽  
Normed Space ◽  
The Other ◽  
Space Structures ◽  
Operator Spaces ◽  
Infinite Dimensions ◽  
Schatten Classes ◽  
Lp Spaces ◽  
First Order ◽  
Order Language

AbstractIt is shown that Schatten p-classes of operators between Hilbert spaces of different (infinite) dimensions have ultrapowers which are (completely) isometric to non-commutative Lp-spaces. On the other hand, these Schatten classes are not themselves isomorphic to non-commutative Lp spaces. As a consequence, the class of non-commutative Lp-spaces is not axiomatizable in the first-order language developed by Henson and Iovino for normed space structures, neither in the signature of Banach spaces, nor in that of operator spaces. Other examples of the same phenomenon are presented that belong to the class of corners of non-commutative Lp-spaces. For p = 1 this last class, which is the same as the class of preduals of ternary rings of operators, is itself axiomatizable in the signature of operator spaces.

Characterizations of Axiomatic Categories of Models Canonically Isomorphic to (Quasi-)Varieties

1988 ◽  
Vol 31 (3) ◽  
pp. 287-300 ◽  
Author(s):  
Michel Hébert
Keyword(s):  
Forgetful Functor ◽  
Canonical Isomorphism ◽  
First Order ◽  
Order Language ◽  
Algebraic Language ◽  
Algebraic Constructions

AbstractLet be the category of all homomorphisms (i.e. functions preserving satisfaction of atomic formulas) between models of a set of sentences T in a finitary first-order language L. Functors between two such categories are said to be canonical if they commute with the forgetful functors. The following properties are characterized syntactically and also in terms of closure of for some algebraic constructions (involving products, equalizers, factorizations and kernel pairs): There is a canonical isomorphism from to a variety (resp. quasivariety) in a finitary expansion of L which assigns to a model its (unique) expansion. This solves a problem of H. Volger.In the case of a purely algebraic language, the properties are equivalent to:“ is canonically isomorphic to a finitary variety (resp. quasivariety)” and, for the variety case, to “the forgetful functor of is monadic (tripleable)”.

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