scholarly journals Finite Model Finding Using the Logic of Equality with Uninterpreted Functions

2016 ◽  
pp. 677-693 ◽  
Author(s):  
Amirhossein Vakili ◽  
Nancy A. Day
Keyword(s):  
Finite Model ◽  
Model Finding

scholarly journals Symmetry Avoidance in MACE-Style Finite Model Finding

2019 ◽  
pp. 3-21 ◽  
Author(s):  
Giles Reger ◽  
Martin Riener ◽  
Martin Suda
Keyword(s):  
Finite Model ◽  
Model Finding

scholarly journals Finite Model Finding in SMT

2013 ◽  
pp. 640-655 ◽  
Author(s):  
Andrew Reynolds ◽  
Cesare Tinelli ◽  
Amit Goel ◽  
Sava Krstić
Keyword(s):  
Finite Model ◽  
Model Finding

Quantifier Instantiation Techniques for Finite Model Finding in SMT

2013 ◽  
pp. 377-391 ◽  
Author(s):  
Andrew Reynolds ◽  
Cesare Tinelli ◽  
Amit Goel ◽  
Sava Krstić ◽  
Morgan Deters ◽  
...  
Keyword(s):  
Finite Model ◽  
Model Finding ◽  
Quantifier Instantiation

scholarly journals Revisiting Question Answering in Vampire

10.29007/fjc4 ◽  
2018 ◽  
Author(s):  
Giles Reger
Keyword(s):  
Question Answering ◽  
Theorem Prover ◽  
Finite Model ◽  
Future Directions ◽  
Model Finding

Question answering is the process of taking a conjecture existentially quantified at the outer- most level and providing one or more instantiations of the quantified variable(s) as a form of an answer to the implied question. For example, given the axioms p(a) and f(a)=a the question ?[X] : p(f(X)) could return the answer X=a. This paper reviews the question answering prob- lem focussing on how it is tackled within the VAMPIRE theorem prover. It covers how VAMPIRE extracts single answers, multiple answers, disjunctive answers, and answers involving theories such as arithmetic. The paper finishes by considering possible future directions, such as integration with finite model finding.

scholarly journals Constraint solving for finite model finding in SMT solvers

2017 ◽  
Vol 17 (4) ◽  
pp. 516-558
Author(s):  
ANDREW REYNOLDS ◽  
CESARE TINELLI ◽  
CLARK BARRETT
Keyword(s):  
Automated Reasoning ◽  
State Of The Art ◽  
Satisfiability Modulo Theories ◽  
Constraint Solving ◽  
Automated Verification ◽  
Finite Model ◽  
Cardinality Constraints ◽  
On Demand ◽  
Smt Solvers ◽  
Model Finding

AbstractSatisfiability modulo theories (SMT) solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing SMT solvers to report “unknown” when they fail to prove the unsatisfiability of a formula with quantifiers. This inability to return counter models limits their usefulness in applications that produce queries involving quantified formulas. In this paper, we reduce these limitations by integrating finite model finding techniques based on constraint solving into the architecture used by modern SMT solvers. This approach is made possible by a novel solver for cardinality constraints, as well as techniques for on-demand instantiation of quantified formulas. Experiments show that our approach is competitive with the state of the art in SMT, and orthogonal to approaches in automated theorem proving.

Finite Model Theory

1995 ◽  
Author(s):  
Heinz-Dieter Ebbinghaus ◽  
Jörg Flum
Keyword(s):  
Model Theory ◽  
Finite Model ◽  
Finite Model Theory

scholarly journals A spatio-temporal specification language and its completeness & decidability

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Tengfei Li ◽  
Jing Liu ◽  
Haiying Sun ◽  
Xiang Chen ◽  
Lipeng Zhang ◽  
...  
Keyword(s):  
Intelligent Transportation System ◽  
Cyber Physical Systems ◽  
Specification Language ◽  
Finite Model ◽  
Critical Systems ◽  
Physical Systems ◽  
Spatial Objects ◽  
Temporal Properties ◽  
Spatio Temporal ◽  
Temporal Specification

AbstractIn the past few years, significant progress has been made on spatio-temporal cyber-physical systems in achieving spatio-temporal properties on several long-standing tasks. With the broader specification of spatio-temporal properties on various applications, the concerns over their spatio-temporal logics have been raised in public, especially after the widely reported safety-critical systems involving self-driving cars, intelligent transportation system, image processing. In this paper, we present a spatio-temporal specification language, STSL PC, by combining Signal Temporal Logic (STL) with a spatial logic S4 u, to characterize spatio-temporal dynamic behaviors of cyber-physical systems. This language is highly expressive: it allows the description of quantitative signals, by expressing spatio-temporal traces over real valued signals in dense time, and Boolean signals, by constraining values of spatial objects across threshold predicates. STSL PC combines the power of temporal modalities and spatial operators, and enjoys important properties such as finite model property. We provide a Hilbert-style axiomatization for the proposed STSL PC and prove the soundness and completeness by the spatio-temporal extension of maximal consistent set and canonical model. Further, we demonstrate the decidability of STSL PC and analyze the complexity of STSL PC. Besides, we generalize STSL to the evolution of spatial objects over time, called STSL OC, and provide the proof of its axiomatization system and decidability.

Canonical rules

2009 ◽  
Vol 74 (4) ◽  
pp. 1171-1205 ◽  
Author(s):  
Emil Jeřábek
Keyword(s):  
Alternative Proof ◽  
Finite Model ◽  
Consequence Relations ◽  
Model Property ◽  
Finite Model Property ◽  
Admissible Rules ◽  
Superintuitionistic Logics ◽  
Canonical Formulas ◽  
Global Consequence

AbstractWe develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia theorem and the theory of modal companions to systems of multiple-conclusion rules or (unitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property.

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