Towards a Maude tool for model checking temporal graph properties

We present our prototypical tool for the verification of graph transformation systems. The major novelty of our tool is that it provides a model checker for temporal graph properties based on counterpart semantics for quantified m-calculi. Our tool can be considered as an instantiation of our approach to counterpart semantics which allows for a neat handling of creation, deletion and merging in systems with dynamic structure. Our implementation is based on the object-based machinery of Maude, which provides the basics to deal with attributed graphs. Graph transformation systems are specified with term rewrite rules. The model checker evaluates logical formulae of second-order modal m-calculus in the automatically generated CounterpartModel (a sort of unfolded graph transition system) of the graph transformation system under study. The result of evaluating a formula is a set of assignments for each state, associating node variables to actual nodes

Semantic Matchmaking as Non-Monotonic Reasoning: A Description Logic Approach

Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the objective of a matchmaking process is to discover best available offers to a given request. We address the problem of matchmaking from a knowledge representation perspective, with a formalization based on Description Logics. We devise Concept Abduction and Concept Contraction as non-monotonic inferences in Description Logics suitable for modeling matchmaking in a logical framework, and prove some related complexity results. We also present reasonable algorithms for semantic matchmaking based on the devised inferences, and prove that they obey to some commonsense properties. Finally, we report on the implementation of the proposed matchmaking framework, which has been used both as a mediator in e-marketplaces and for semantic web services discovery

Ontology-based data access with databases: a short course

Ontology-based data access (OBDA) is regarded as a key ingredient of the new generation of information systems. In the OBDA paradigm, an ontology defines a high-level global schema of (already existing) data sources and provides a vocabulary for user queries. An OBDA system rewrites such queries and ontologies into the vocabulary of the data sources and then delegates the actual query evaluation to a suitable query answering system such as a relational database management system or a datalog engine. In this chapter, we mainly focus on OBDA with the ontology language OWL 2QL, one of the three profiles of the W3C standard Web Ontology Language OWL 2, and relational databases, although other possible languages will also be discussed. We consider different types of conjunctive query rewriting and their succinctness, different architectures of OBDA systems, and give an overview of the OBDA system Ontop

A Universal Machine for Biform Theory Graphs

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time. We pick up on the idea of biform theories and interpret it in the MMTt/OMDoc framework which introduced the foundations-as-theories approach, and can thus represent both logics and programming languages as theories. This yields a formal, modular framework of biform theory graphs which mixes specifications and implementations sharing the module system and typing information. We present automated knowledge management work flows that interface to existing specification/programming tools and enable an OpenMath Machine, that operationalizes biform theories, evaluating expressions by exhaustively applying the implementations of the respective operators. We evaluate the new biform framework by adding implementations to the OpenMath standard content dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final publication is available at http://link.springer.com

Conservativity of embeddings in the lambda Pi calculus modulo rewriting (long version)

The lambda Pi calculus can be extended with rewrite rules to embed any functional pure type system. In this paper, we show that the embedding is conservative by proving a relative form of normalization, thus justifying the use of the lambda Pi calculus modulo rewriting as a logical framework for logics based on pure type systems. This result was previously only proved under the condition that the target system is normalizing. Our approach does not depend on this condition and therefore also works when the source system is not normalizing.Comment: Long version of TLCA 2015 pape