900 research outputs found
Goal Translation for a Hammer for Coq (Extended Abstract)
Hammers are tools that provide general purpose automation for formal proof
assistants. Despite the gaining popularity of the more advanced versions of
type theory, there are no hammers for such systems. We present an extension of
the various hammer components to type theory: (i) a translation of a
significant part of the Coq logic into the format of automated proof systems;
(ii) a proof reconstruction mechanism based on a Ben-Yelles-type algorithm
combined with limited rewriting, congruence closure and a first-order
generalization of the left rules of Dyckhoff's system LJT.Comment: In Proceedings HaTT 2016, arXiv:1606.0542
Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support
A framework and methodology---termed LogiKEy---for the design and engineering
of ethical reasoners, normative theories and deontic logics is presented. The
overall motivation is the development of suitable means for the control and
governance of intelligent autonomous systems. LogiKEy's unifying formal
framework is based on semantical embeddings of deontic logics, logic
combinations and ethico-legal domain theories in expressive classic
higher-order logic (HOL). This meta-logical approach enables the provision of
powerful tool support in LogiKEy: off-the-shelf theorem provers and model
finders for HOL are assisting the LogiKEy designer of ethical intelligent
agents to flexibly experiment with underlying logics and their combinations,
with ethico-legal domain theories, and with concrete examples---all at the same
time. Continuous improvements of these off-the-shelf provers, without further
ado, leverage the reasoning performance in LogiKEy. Case studies, in which the
LogiKEy framework and methodology has been applied and tested, give evidence
that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure
Induction of First-Order Decision Lists: Results on Learning the Past Tense of English Verbs
This paper presents a method for inducing logic programs from examples that
learns a new class of concepts called first-order decision lists, defined as
ordered lists of clauses each ending in a cut. The method, called FOIDL, is
based on FOIL (Quinlan, 1990) but employs intensional background knowledge and
avoids the need for explicit negative examples. It is particularly useful for
problems that involve rules with specific exceptions, such as learning the
past-tense of English verbs, a task widely studied in the context of the
symbolic/connectionist debate. FOIDL is able to learn concise, accurate
programs for this problem from significantly fewer examples than previous
methods (both connectionist and symbolic).Comment: See http://www.jair.org/ for any accompanying file
Optimal Planning Modulo Theories
Planning for real-world applications requires algorithms and tools with the ability to handle the complexity such scenarios entail. However, meeting the needs of such applications poses substantial challenges, both representational and algorithmic. On the one hand, expressive languages are needed to build faithful models. On the other hand, efficient solving techniques that can support these languages need to be devised. A response to this challenge is underway, and the past few years witnessed a community effort towards more expressive languages, including decidable fragments of first-order theories. In this work we focus on planning with arithmetic theories and propose Optimal Planning Modulo Theories, a framework that attempts to provide efficient means of dealing with such problems. Leveraging generic Optimization Modulo Theories (OMT) solvers, we first present domain-specific encodings for optimal planning in complex logistic domains. We then present a more general, domain- independent formulation that allows to extend OMT planning to a broader class of well-studied numeric problems in planning. To the best of our knowledge, this is the first time OMT procedures are employed in domain-independent planning
Disjunctive ASP with Functions: Decidable Queries and Effective Computation
Querying over disjunctive ASP with functions is a highly undecidable task in
general. In this paper we focus on disjunctive logic programs with stratified
negation and functions under the stable model semantics (ASP^{fs}). We show
that query answering in this setting is decidable, if the query is finitely
recursive (ASP^{fs}_{fr}). Our proof yields also an effective method for query
evaluation. It is done by extending the magic set technique to ASP^{fs}_{fr}.
We show that the magic-set rewritten program is query equivalent to the
original one (under both brave and cautious reasoning). Moreover, we prove that
the rewritten program is also finitely ground, implying that it is decidable.
Importantly, finitely ground programs are evaluable using existing ASP solvers,
making the class of ASP^{fs}_{fr} queries usable in practice.Comment: 16 pages, 1 figur
Ensuring Query Compatibility with Evolving XML Schemas
During the life cycle of an XML application, both schemas and queries may
change from one version to another. Schema evolutions may affect query results
and potentially the validity of produced data. Nowadays, a challenge is to
assess and accommodate the impact of theses changes in rapidly evolving XML
applications.
This article proposes a logical framework and tool for verifying
forward/backward compatibility issues involving schemas and queries. First, it
allows analyzing relations between schemas. Second, it allows XML designers to
identify queries that must be reformulated in order to produce the expected
results across successive schema versions. Third, it allows examining more
precisely the impact of schema changes over queries, therefore facilitating
their reformulation
More SPASS with Isabelle: superposition with hard sorts and configurable simplification
Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammerâs success rate. The main enhancements are native support for hard sorts (simple types) in SPASS, simplification that honors the orientation of Isabelle simp rules, and a pair of clause-selection strategies targeted at large lemma libraries. The usefulness of this integration is confirmed by an evaluation on a vast benchmark suite and by a
case study featuring a formalization of language-based security
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