scholarly journals Interpreting GPFCSP within the LΠ ½ logic framework

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 889-897
Author(s):  
Aleksandar Takaci ◽  
Aleksandar Perovic ◽  
Aleksandar Jovanovic
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Complete Axiomatization ◽  
Interpretation Method

The aim of this paper is to interpret Generalized Priority Constraint Satisfaction Problem (GPFCSP) using the interpretational method. We will interpret the L? ? logic into the first order theory of the reals, in order to obtain alternative, simple-complete axiomatization of L? ? logic. A complete axiomatization using the interpretation method as a syntactical approach is given.

scholarly journals Automated reasoning-alternative methods

2004 ◽  
Vol 1 (3) ◽  
pp. 15-20
Author(s):  
Aleksandar Perovic ◽  
Nedeljko Stefanovic ◽  
Milos Milosevic ◽  
Dejan Ilic
Keyword(s):  
Automated Reasoning ◽  
Quantifier Elimination ◽  
Order Theory ◽  
Alternative Methods ◽  
Formal Representation ◽  
First Order ◽  
First Order Theory ◽  
Interpretation Method

Our main goal is to describe a potential usage of the interpretation method (i.e. formal representation of one first order theory into another) together with quantifier elimination procedures developed in the GIS.

scholarly journals Permutation groups with small orbit growth

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manuel Bodirsky ◽  
Bertalan Bodor
Keyword(s):  
Automorphism Group ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Permutation Groups ◽  
First Order ◽  
Finite Covers

Abstract Let K exp + \mathcal{K}_{{\operatorname{exp}}{+}} be the class of all structures 𝔄 such that the automorphism group of 𝔄 has at most c ⁢ n d ⁢ n cn^{dn} orbits in its componentwise action on the set of 𝑛-tuples with pairwise distinct entries, for some constants c , d c,d with d < 1 d<1 . We show that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of finite covers of first-order reducts of unary structures, and also that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of first-order reducts of finite covers of unary structures. It follows that the class of first-order reducts of finite covers of unary structures is closed under taking model companions and model-complete cores, which is an important property when studying the constraint satisfaction problem for structures from K exp + \mathcal{K}_{{\operatorname{exp}}{+}} . We also show that Thomas’ conjecture holds for K exp + \mathcal{K}_{{\operatorname{exp}}{+}} : all structures in K exp + \mathcal{K}_{{\operatorname{exp}}{+}} have finitely many first-order reducts up to first-order interdefinability.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory

The spectrum of resplendency

1990 ◽  
Vol 55 (2) ◽  
pp. 626-636
Author(s):  
John T. Baldwin
Keyword(s):  
Homogeneous Model ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Uncountable Cardinal ◽  
Recursive Theory ◽  
Finite Language

AbstractLet T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.

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