354 research outputs found
A CDCL-style calculus for solving non-linear constraints
In this paper we propose a novel approach for checking satisfiability of
non-linear constraints over the reals, called ksmt. The procedure is based on
conflict resolution in CDCL style calculus, using a composition of symbolical
and numerical methods. To deal with the non-linear components in case of
conflicts we use numerically constructed restricted linearisations. This
approach covers a large number of computable non-linear real functions such as
polynomials, rational or trigonometrical functions and beyond. A prototypical
implementation has been evaluated on several non-linear SMT-LIB examples and
the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at
<http://informatik.uni-trier.de/~brausse/ksmt/
Graph Sequence Learning for Premise Selection
Premise selection is crucial for large theory reasoning as the sheer size of
the problems quickly leads to resource starvation. This paper proposes a
premise selection approach inspired by the domain of image captioning, where
language models automatically generate a suitable caption for a given image.
Likewise, we attempt to generate the sequence of axioms required to construct
the proof of a given problem. This is achieved by combining a pre-trained graph
neural network with a language model. We evaluated different configurations of
our method and experience a 17.7% improvement gain over the baseline.Comment: 17 page
Heterogeneous Heuristic Optimisation and Scheduling for First-Order Theorem Proving
Good heuristics are essential for successful proof search in first-order automated theorem proving. As a result, state-of-the-art theorem provers offer a range of options for tuning the proof search process to specific problems. However, the vast configuration space makes it exceedingly challenging to construct effective heuristics. In this paper we present a new approach called HOS-ML, for automatically discovering new heuristics and mapping problems into optimised local schedules comprising of these heuristics. Our approach is based on interleaving Bayesian hyper-parameter optimisation for discovering promising heuristics and dynamic clustering to make optimisation efficient on heterogeneous problems. HOS-ML also use constraint programming to devise locally optimal schedules and machine learning for mapping unseen problems into such schedules. We evaluated HOS-ML on the theorem prover iProver and demonstrated that it can discover new heuristics that considerably improve performance and can solve problems that have not been solved previously by any other system.<br/
Scavenger 0.1: A Theorem Prover Based on Conflict Resolution
This paper introduces Scavenger, the first theorem prover for pure
first-order logic without equality based on the new conflict resolution
calculus. Conflict resolution has a restricted resolution inference rule that
resembles (a first-order generalization of) unit propagation as well as a rule
for assuming decision literals and a rule for deriving new clauses by (a
first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201
Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints
The monadic shallow linear Horn fragment is well-known to be decidable and
has many application, e.g., in security protocol analysis, tree automata, or
abstraction refinement. It was a long standing open problem how to extend the
fragment to the non-Horn case, preserving decidability, that would, e.g.,
enable to express non-determinism in protocols. We prove decidability of the
non-Horn monadic shallow linear fragment via ordered resolution further
extended with dismatching constraints and discuss some applications of the new
decidable fragment.Comment: 29 pages, long version of CADE-26 pape
Delocalization of Wannier-Stark ladders by phonons: tunneling and stretched polarons
We study the coherent dynamics of a Holstein polaron in strong electric
fields. A detailed analytical and numerical analysis shows that even for small
hopping constant and weak electron-phonon interaction, polaron states can
become delocalized if a resonance condition develops between the original
Wannier-Stark states and the phonon modes, yielding both tunneling and
`stretched' polarons. The unusual stretched polarons are characterized by a
phonon cloud that {\em trails} the electron, instead of accompanying it. In
general, our novel approach allows us to show that the polaron spectrum has a
complex nearly-fractal structure, due to the coherent coupling between states
in the Cayley tree which describes the relevant Hilbert space. The eigenstates
of a finite ladder are analyzed in terms of the observable tunneling and
optical properties of the system.Comment: 7 pages, 4 figure
First-Order Logic Theorem Proving and Model Building via Approximation and Instantiation
In this paper we consider first-order logic theorem proving and model
building via approximation and instantiation. Given a clause set we propose its
approximation into a simplified clause set where satisfiability is decidable.
The approximation extends the signature and preserves unsatisfiability: if the
simplified clause set is satisfiable in some model, so is the original clause
set in the same model interpreted in the original signature. A refutation
generated by a decision procedure on the simplified clause set can then either
be lifted to a refutation in the original clause set, or it guides a refinement
excluding the previously found unliftable refutation. This way the approach is
refutationally complete. We do not step-wise lift refutations but conflicting
cores, finite unsatisfiable clause sets representing at least one refutation.
The approach is dual to many existing approaches in the literature because our
approximation preserves unsatisfiability
Learning Instantiation in First-Order Logic
Contains fulltext :
286055.pdf (Publisher’s version ) (Open Access)AITP 202
AC-KBO Revisited
Equational theories that contain axioms expressing associativity and
commutativity (AC) of certain operators are ubiquitous. Theorem proving methods
in such theories rely on well-founded orders that are compatible with the AC
axioms. In this paper we consider various definitions of AC-compatible
Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are
revisited. The former is enhanced to a more powerful version, and we modify the
latter to amend its lack of monotonicity on non-ground terms. We further
present new complexity results. An extension reflecting the recent proposal of
subterm coefficients in standard Knuth-Bendix orders is also given. The various
orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming
(TPLP) special issue for the 12th International Symposium on Functional and
Logic Programming (FLOPS 2014
Finding Finite Models in Multi-Sorted First-Order Logic
This work extends the existing MACE-style finite model finding approach to
multi-sorted first order logic. This existing approach iteratively assumes
increasing domain sizes and encodes the related ground problem as a SAT
problem. When moving to the multi-sorted setting each sort may have a different
domain size, leading to an explosion in the search space. This paper focusses
on methods to tame that search space. The key approach adds additional
information to the SAT encoding to suggest which domains should be grown.
Evaluation of an implementation of techniques in the Vampire theorem prover
shows that they dramatically reduce the search space and that this is an
effective approach to find finite models in multi-sorted first order logic.Comment: SAT 201
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