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 Exploring Steinitz-Rademacher Polyhedra: a Challenge for Automated Reasoning Tools

10.29007/d3ls ◽  
2018 ◽  
Author(s):  
Jesse Alama
Keyword(s):  
Automated Reasoning ◽  
Order Theory ◽  
Incidence Structures ◽  
First Order ◽  
First Order Theory

This note reports on some experiments, using a handful of standard automated reasoning tools, for exploring Steinitz-Rademacher polyhedra, which are models of a certain first-order theory of incidence structures. This theory and its models, even simple ones, presents significant, geometrically fascinating challenges for automated reasoning tools are.

More on definable sets of p-adic numbers

1988 ◽  
Vol 53 (3) ◽  
pp. 912-920 ◽  
Author(s):  
Philip Scowcroft
Keyword(s):  
Cross Section ◽  
Quantifier Elimination ◽  
Order Theory ◽  
Model Completeness ◽  
First Order ◽  
First Order Theory ◽  
Ordered Fields ◽  
Definable Sets ◽  
The Cross ◽  
Primitive Recursive

To eliminate quantifiers in the first-order theory of the p-adic field Qp, Ax and Kochen use a language containing a symbol for a cross-section map n → pn from the value group Z into Qp [1, pp. 48–49]. The primitive-recursive quantifier eliminations given by Cohen [2] and Weispfenning [10] also apply to a language mentioning the cross-section, but none of these authors seems entirely happy with his results. As Cohen says, “all the operations… introduced for our simple functions seem natural, with the possible exception of the map n → pn” [2, p. 146]. So all three authors show that various consequences of quantifier elimination—completeness, decidability, model-completeness—also hold for a theory of Qp not employing the cross-section [1, p. 453; 2, p. 146; 10, §4]. Macintyre directs a more specific complaint against the cross-section [5, p. 605]. Elementary formulae which use it can define infinite discrete subsets of Qp; yet infinite discrete subsets of R are not definable in the language of ordered fields, and so certain analogies between Qp and R suggested by previous model-theoretic work seem to break down.To avoid this problem, Macintyre gives up the cross-section and eliminates quantifiers in a theory of Qp written just in the usual language of fields supplemented by a predicate V for Qp's valuation ring and by predicates Pn for the sets of nth powers in Qp (for all n ≥ 2).

scholarly journals SOME PROPERTIES OF ANALYTIC DIFFERENCE VALUED FIELDS

2015 ◽  
Vol 16 (3) ◽  
pp. 447-499 ◽  
Author(s):  
Silvain Rideau
Keyword(s):  
Algebraic Closure ◽  
Quantifier Elimination ◽  
Order Theory ◽  
Analytic Structure ◽  
Independence Property ◽  
Valued Fields ◽  
First Order ◽  
Witt Vectors ◽  
First Order Theory

We prove field quantifier elimination for valued fields endowed with both an analytic structure that is $\unicode[STIX]{x1D70E}$-Henselian and an automorphism that is $\unicode[STIX]{x1D70E}$-Henselian. From this result we can deduce various Ax–Kochen–Eršov type results with respect to completeness and the independence property. The main example we are interested in is the field of Witt vectors on the algebraic closure of $\mathbb{F}_{p}$ endowed with its natural analytic structure and the lifting of the Frobenius. It turns out we can give a (reasonable) axiomatization of its first-order theory and that this theory does not have the independence property.

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.

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