Beyond First-Order Satisfaction: Fixed Points, Interpolants, Automata and Polynomials

2012 ◽  
pp. 1-6 ◽  
Author(s):  
Thomas Ball ◽  
Nikolaj Bjørner ◽  
Leonardo de Moura ◽  
Kenneth L. McMillan ◽  
Margus Veanes
Keyword(s):  
Fixed Points ◽  
First Order

scholarly journals Extensions in graph normal form

2020 ◽  
Author(s):  
Michał Walicki
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
Propositional Logic ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Special Cases

Abstract Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.

scholarly journals Fixed Points of Meromorphic Functions and Their Higher Order Differences and Shifts

2019 ◽  
Vol 17 (1) ◽  
pp. 677-688 ◽  
Author(s):  
Hai-Ying Chen ◽  
Xiu-Min Zheng
Keyword(s):  
Fixed Points ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Order Difference ◽  
First Order ◽  
Special Points ◽  
And Shifts

Abstract In this paper, we investigate the relationships between fixed points of meromorphic functions, and their higher order differences and shifts, and generalize the case of fixed points into the more general case for first order difference and shift. Concretely, some estimates on the order and the exponents of convergence of special points of meromorphic functions and their differences and shifts are obtained.

Evidences of the Instability Fixed Points of First-Order Phase Transitions

2011 ◽  
Vol 143 (6) ◽  
pp. 1136-1153 ◽  
Author(s):  
Shuangli Fan ◽  
Fan Zhong
Keyword(s):  
Phase Transitions ◽  
Fixed Points ◽  
First Order ◽  
First Order Phase

Absolute surface manometry: thermodynamic fixed points for air-water monolayers of pentadecanoic acid at 25°C

1984 ◽  
Vol 396 (1810) ◽  
pp. 143-154 ◽  
Keyword(s):  
Phase Transitions ◽  
Fixed Points ◽  
High Purity ◽  
Pentadecanoic Acid ◽  
Hexadecanoic Acid ◽  
First Order ◽  
Extensive Data ◽  
Series Of Experiments

An extensive series of experiments on pentadecanoic acid monolayers has been made at 25°C with several independent methods of surface manometry. The purpose of the study was to establish a set of surface pressures for the three monolayer phase transitions to act as surface manometric standards. It was coincidentally demonstrated in high purity systems that the so-called liquid-expanded-liquid-condensed transition is simply first order. The experimental requirements for reproducible surface manometry are described. Less extensive data on hexadecanoic acid are also given to invite further critical experiments.

Fixed point theorems for a pair of single-valued operators in a metric space endowed with a reflexive relation

2017 ◽  
Vol 33 (3) ◽  
pp. 301-310
Author(s):  
MELANIA-IULIA DOBRICAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Theorems ◽  
Mixed Monotone Property ◽  
First Order ◽  
System Equation ◽  
Coupled Fixed Points

In this paper we provide some existence and uniqueness theorems for coupled fixed points for a pair of contractive operators satisfying a mixed monotone property, in a metric space endowed with a reflexive relation. An application to a first-order differential system equation with PBV conditions is also given to illustrate the utility of our results.

Minimal predicates, fixed-points, and definability

2005 ◽  
Vol 70 (3) ◽  
pp. 696-712 ◽  
Author(s):  
Johan Van Benthem
Keyword(s):  
Mathematical Logic ◽  
Fixed Points ◽  
Expressive Power ◽  
Correspondence Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Technical Result ◽  
Unique Existence ◽  
First Order ◽  
Preservation Theorem

AbstractMinimal predicates P satisfying a given first-order description ϕ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order ‘PIA conditions’ ϕ(P) which guarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of ‘predicate intersection’. Next, we show how iterated predicate minimization on PIA-conditions yields a language MIN(FO) equal in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond.

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