116 research outputs found
A Posthumous Contribution by {Larry Wos}: {E}xcerpts from an Unpublished Column
International audienceShortly before Larry Wos passed away, he sent a manuscript for discussion to Sophie Tourret, the editor of the AAR newsletter. We present excerpts from this final manuscript, put it in its historic context and explain its relevance for today’s research in automated reasoning
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
On Deciding Local Theory Extensions via E-matching
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures
for theories of data types that commonly occur in software. This makes them
important tools for automating verification problems. A limitation frequently
encountered is that verification problems are often not fully expressible in
the theories supported natively by the solvers. Many solvers allow the
specification of application-specific theories as quantified axioms, but their
handling is incomplete outside of narrow special cases.
In this work, we show how SMT solvers can be used to obtain complete decision
procedures for local theory extensions, an important class of theories that are
decidable using finite instantiation of axioms. We present an algorithm that
uses E-matching to generate instances incrementally during the search,
significantly reducing the number of generated instances compared to eager
instantiation strategies. We have used two SMT solvers to implement this
algorithm and conducted an extensive experimental evaluation on benchmarks
derived from verification conditions for heap-manipulating programs. We believe
that our results are of interest to both the users of SMT solvers as well as
their developers
Connection-Minimal Abduction in {E}L via Translation to {FOL} (Extended Abstract)
International audienceAbduction in description logics finds extensions of a knowledge base to make it entail an observation. As such, it can be used to explain why the observation does not follow, to repair incomplete knowledge bases, and to provide possible explanations for unexpected observations. We consider TBox abduction in the lightweight description logic EL , where the observation is a concept inclusion and the background knowledge is a TBox, i.e., a set of concept inclusions. To avoid useless answers, such problems usually come with further restrictions on the solution space and/or minimality criteria that help sort the chaff from the grain. We argue that existing minimality notions are insufficient, and introduce connection minimality. This criterion follows Occam’s razor by rejecting hypotheses that use concept inclusions unrelated to the problem at hand. We show how to compute a special class of connection-minimal hypotheses in a sound and complete way. Our technique is based on a translation to first-order logic, and constructs hypotheses based on prime implicates. We evaluate a prototype implementation of our approach on ontologies from the medical domain
On the Verification of Parametric Systems
We present an approach to the verification of systems for whose description
some elements - constants or functions - are underspecified and can be regarded
as parameters, and, in particular, describe a method for automatically
generating constraints on such parameters under which certain safety conditions
are guaranteed to hold. We present an implementation and illustrate its use on
several examples.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1910.0520
Graph Based Reduction of Program Verification Conditions
Increasing the automaticity of proofs in deductive verification of C programs
is a challenging task. When applied to industrial C programs known heuristics
to generate simpler verification conditions are not efficient enough. This is
mainly due to their size and a high number of irrelevant hypotheses. This work
presents a strategy to reduce program verification conditions by selecting
their relevant hypotheses. The relevance of a hypothesis is determined by the
combination of a syntactic analysis and two graph traversals. The first graph
is labeled by constants and the second one by the predicates in the axioms. The
approach is applied on a benchmark arising in industrial program verification
Delta-Decision Procedures for Exists-Forall Problems over the Reals
Solving nonlinear SMT problems over real numbers has wide applications in
robotics and AI. While significant progress is made in solving quantifier-free
SMT formulas in the domain, quantified formulas have been much less
investigated. We propose the first delta-complete algorithm for solving
satisfiability of nonlinear SMT over real numbers with universal quantification
and a wide range of nonlinear functions. Our methods combine ideas from
counterexample-guided synthesis, interval constraint propagation, and local
optimization. In particular, we show how special care is required in handling
the interleaving of numerical and symbolic reasoning to ensure
delta-completeness. In experiments, we show that the proposed algorithms can
handle many new problems beyond the reach of existing SMT solvers
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