scholarly journals New Techniques in Clausal Form Generation

10.29007/dzfz ◽  
2018 ◽  
Author(s):  
Giles Reger ◽  
Martin Suda ◽  
Andrei Voronkov
Keyword(s):  
Normal Form ◽  
Automated Reasoning ◽  
Contextual Information ◽  
Experimental Results ◽  
Large Impact ◽  
Top Down ◽  
New Techniques ◽  
First Order ◽  
Form Generation ◽  
Proof Search

In automated reasoning it is common that first-order formulas need to be translated into clausal normal form for proof search. The structure of this normal form can have a large impact on the performance of first-order theorem provers, influencing whether a proof can be found and how quickly. It is common folklore that transformations should ideally minimise both the size of the generated clause set and extensions to the signature. This paper introduces a new top-down approach to clausal form generation for first-order formulas that aims to achieve this goal in a new way. The main advantage of this approach over existing bottom-up techniques is that more contextual information is available at points where decisions such as subformula-naming and Skolemisation occur. Experimental results show that our implementation of the transformation in Vampire can lead to clausal forms which are smaller and better suited to proof search.

scholarly journals Prime Implicate Generation in Equational Logic (extended abstract)

2018 ◽  
Author(s):  
Mnacho Echenim ◽  
Nicolas Peltier ◽  
Sophie Tourret
Keyword(s):  
State Of The Art ◽  
Experimental Results ◽  
Equational Logic ◽  
First Order ◽  
On Demand ◽  
Proof Search ◽  
Superposition Calculus

A procedure is proposed to efficiently generate sets of ground implicates of first-order formulas with equality. It is based on a tuning of the superposition calculus, enriched with rules that add new hypotheses on demand during the proof search. Experimental results are presented, showing that the proposed approach is more efficient than state-of-the-art systems.

Physical Failure Analysis Techniques for Front-End-of-Line Defect Analysis

2016 ◽  
Author(s):  
Dirk Doyle ◽  
Lawrence Benedict ◽  
Fritz Christian Awitan
Keyword(s):  
Cross Section ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Gate Oxide ◽  
Top Down ◽  
New Techniques ◽  
First Case ◽  
Transmission Electron ◽  
Scanning Transmission

Abstract Novel techniques to expose substrate-level defects are presented in this paper. New techniques such as inter-layer dielectric (ILD) thinning, high keV imaging, and XeF2 poly etch overflow are introduced. We describe these techniques as applied to two different defects types at FEOL. In the first case, by using ILD thinning and high keV imaging, coupled with focused ion beam (FIB) cross section and scanning transmission electron microscopy (STEM,) we were able to judge where to sample for TEM from a top down perspective while simultaneously providing the top down images giving both perspectives on the same sample. In the second case we show retention of the poly Si short after removal of CoSi2 formation on poly. Removal of the CoSi2 exposes the poly Si such that we can utilize XeF2 to remove poly without damaging gate oxide to reveal pinhole defects in the gate oxide. Overall, using these techniques have led to 1) increased chances of successfully finding the defects, 2) better characterization of the defects by having a planar view perspective and 3) reduced time in localizing defects compared to performing cross section alone.

Interfacial mass transfer in turbulent flow accompanied by irreversible first order chemical reaction

1979 ◽  
Vol 44 (5) ◽  
pp. 1388-1396
Author(s):  
Václav Kolář ◽  
Zdeněk Brož
Keyword(s):  
Mass Transfer ◽  
Turbulent Flow ◽  
Chemical Reaction ◽  
Experimental Results ◽  
Theoretical Concepts ◽  
First Order ◽  
Order Chemical Reaction ◽  
Interfacial Mass Transfer ◽  
First Order Chemical Reaction

Relations describing the mass transfer accompanied by an irreversible first order chemical reaction are derived, based on the formerly published general theoretical concepts of interfacial mass transfer. These relations are compared with experimental results taken from literature.

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 Model Completeness, Uniform Interpolants and Superposition Calculus

2021 ◽  
Author(s):  
Diego Calvanese ◽  
Silvio Ghilardi ◽  
Alessandro Gianola ◽  
Marco Montali ◽  
Andrey Rivkin
Keyword(s):  
Automated Reasoning ◽  
Quantifier Elimination ◽  
Effective Solution ◽  
Model Completeness ◽  
Present Contribution ◽  
First Order ◽  
Reduction Strategies ◽  
Infinite State Systems ◽  
Infinite State ◽  
Superposition Calculus

AbstractUniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as “covers”) in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by Gulwani and Musuvathi, and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution.

Dynamical theory of neutron diffraction

1978 ◽  
Vol 56 (10) ◽  
pp. 1261-1288 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Neutron Diffraction ◽  
Theoretical Basis ◽  
Dynamical Theory ◽  
Experimental Results ◽  
Neutron Interferometry ◽  
New Techniques ◽  
The Past ◽  
Neutron Optics ◽  
Coherent Wave ◽  
Special Cases

We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schrödinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry, Pendellösung interference, and neutron interferometry.

A Percolation Equation for Modeling Experimental Results for Continuum Percolation Systems

2001 ◽  
Vol 699 ◽  
Author(s):  
D.S. McLachlan ◽  
C. Chiteme ◽  
W.D. Heiss ◽  
Junjie Wu
Keyword(s):  
Experimental Data ◽  
Ac Conductivity ◽  
Volume Fraction ◽  
Power Laws ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Equation ◽  
Scaling Properties ◽  
First Order ◽  
Dc And Ac Conductivity

AbstractThe standard percolation equations or power laws, for dc and ac conductivity (dielectric constant) are based on scaling ansatz, and predict the behaviour of the first and second order terms, above and below the percolation or critical volume fraction (øc), and in the crossoverregion. Recent experimental results on ac conductivity are presented, which show that these equations, with the exception of real σm above øc and the first order terms in the crossover region, are only valid in the limit σi/σc = 0, where for an ideal dielectric σi=ωε0εr.A single analytical equation, which has the same parameters as the standard percolation equations, and which, for ac conductivity, reduces to the standard percolation power laws in the limit σi(ωε0εr)/σc = 0 for all but one case, is presented. The exception is the expression for real σm below øc, where the standard power law is always incorrect. The equation is then shown to quantitatively fit both first and second order dc and ac experimental data over the entire frequency and composition range. This phenomenological equation is also continuous, has the scaling properties required at a second order metal-insulator and fits scaled first order dc and ac experimental data. Unfortunately, the s and t exponents that are necessary to fit the data to the above analytical equation are usually not the simple dimensionally determined universal ones and depend on a number of factors.

scholarly journals CSE_E 1.0: An Integrated Automated Theorem Prover for First-Order Logic

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1142
Author(s):  
Feng Cao ◽  
Yang Xu ◽  
Jun Liu ◽  
Shuwei Chen ◽  
Xinran Ning
Keyword(s):  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
Inference Mechanism ◽  
First Order ◽  
Proof Search ◽  
Interdisciplinary Field ◽  
Heuristic Strategies ◽  
Automated Theorem Prover ◽  
Hard Problems

First-order logic is an important part of mathematical logic, and automated theorem proving is an interdisciplinary field of mathematics and computer science. The paper presents an automated theorem prover for first-order logic, called C S E _ E 1.0, which is a combination of two provers contradiction separation extension (CSE) and E, where CSE is based on the recently-introduced multi-clause standard contradiction separation (S-CS) calculus for first-order logic and E is the well-known equational theorem prover for first-order logic based on superposition and rewriting. The motivation of the combined prover C S E _ E 1.0 is to (1) evaluate the capability, applicability and generality of C S E _ E , and (2) take advantage of novel multi-clause S-CS dynamic deduction of CSE and mature equality handling of E to solve more and harder problems. In contrast to other improvements of E, C S E _ E 1.0 optimizes E mainly from the inference mechanism aspect. The focus of the present work is given to the description of C S E _ E including its S-CS rule, heuristic strategies, and the S-CS dynamic deduction algorithm for implementation. In terms of combination, in order not to lose the capability of E and use C S E _ E to solve some hard problems which are unsolved by E, C S E _ E 1.0 schedules the running of the two provers in time. It runs plain E first, and if E does not find a proof, it runs plain CSE, then if it does not find a proof, some clauses inferred in the CSE run as lemmas are added to the original clause set and the combined clause set handed back to E for further proof search. C S E _ E 1.0 is evaluated through benchmarks, e.g., CASC-26 (2017) and CASC-J9 (2018) competition problems (FOFdivision). Experimental results show that C S E _ E 1.0 indeed enhances the performance of E to a certain extent.

A reduction class containing formulas with one monadic predicate and one binary function symbol

1976 ◽  
Vol 41 (1) ◽  
pp. 45-49
Author(s):  
Charles E. Hughes
Keyword(s):  
Normal Form ◽  
Predicate Symbol ◽  
Conjunctive Normal Form ◽  
Function Symbol ◽  
Predicate Calculus ◽  
Binary Function ◽  
First Order ◽  
The Matrix ◽  
Reduction Class ◽  
Order Predicate Calculus

AbstractA new reduction class is presented for the satisfiability problem for well-formed formulas of the first-order predicate calculus. The members of this class are closed prenex formulas of the form ∀x∀yC. The matrix C is in conjunctive normal form and has no disjuncts with more than three literals, in fact all but one conjunct is unary. Furthermore C contains but one predicate symbol, that being unary, and one function symbol which symbol is binary.

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

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