George Koletsos

Many-valued modal non-monotonic reasoning: sequential stable sets and logics with linear truth spaces

A family of many-valued modal logics which correspond to possible-worlds models with many-valued accessibility relations, has been recently proposed by M. Fitting [7, 8]. Non-monotonic extensions of these logics are introduced with a fixpoint construction a la McDermott & Doyle and employ sequential belief sets as epistemic states [9]. In this paper we take a logical investigation of many-valued modal non-monotonic reasoning in Fittings formal framework. We examine the notion of MV-stable sets which emerges as a sequential many-valued analog of Stalnaker-Moore stable sets and prove that several attractive epistemic properties are essentially retained in the many-valued setting, esp. when focusing on a syntactically simple epistemic fragment of MV-stable sets. We show that MV-stable sets are always closed under S4 consequence and identify three sufficient conditions for capturing axioms of negative introspection. Also, the relation of MV-stable sets to many-valued analogs of classical S5 models and to many-valued extensions of universal models is discussed. Finally, we pay special attention to the subclass of logics built on linear Heyting algebras and show that inside this subclass, the situation is very similar - in many respects - to the machinery devised by W. Marek, G. Schwarz and M. Truszczynski. In particular, the normal fragments of the two important classical ranges of modal non-monotonic logics remain intact: many-valued autoepistemic logic is captured by any non-monotonic logic in K5 - KD45 and many-valued reflexive autoepistemic logic corresponds to KTw5 - Sw5.

Query rewriting under ontology contraction

Conjunctive query (CQ) answering is a key reasoning service for ontology-based data access. One of the most prominent approaches to conjunctive query answering is query rewriting where a wide variety of systems has been proposed the last years. All of them accept as input a fixed CQ q and ontology

Extending standards with formal methods: Open Document Architecture

{\mathcal O}

From ASN.1 into CafeOBJ: Some First Steps

and produce a rewriting for

Towards formal open standards: formalizing a standard's requirements

q, {\mathcal O}

Query Rewriting Under Ontology Change

. However, in many real world applications ontologies are very often dynamic--that is, new axioms can be added or existing ones removed frequently. In this paper we study the problem of computing a rewriting for a CQ over an ontology that has been contracted (i.e., some of its axioms have been removed) given a rewriting for the input CQ and ontology. Our goal is to compute a rewriting directly from the input rewriting and avoid computing one from scratch. We study the problem theoretically and provide sufficient conditions under which this process is possible. Moreover, we present a practical algorithm which we implemented and evaluated against other state-of-the-art systems obtaining encouraging results. Finally, axiom removal can also be relevant to ontology design. For each test ontology we study how much the removal of an axiom affects the size of the rewriting and the performance of systems. If the removal of a single axiom causes a significant decrease either in the size or in the computation time then this part of the ontology can be re-modelled.

Intersection Types and Termination Properties

Formal methods, while very promising, are being adopted by software/protocol engineers very slowly, as the industry has little motivation to move into this new, unknown territory. At the same time, new industrial standards are being released quite frequently, as standardization seems to be very popular among developers. In this paper we present the idea of blending formal methods with industry standards. We claim that this results in more concrete system design and extended property verification tools. The enhancement of industry standards with formal methodologies leads to better understanding of the designed environment, eliminates ambiguity and forces a certain level of precision into the specification. An extra benefit is that we can use one of the many algebraic specification languages in order to assist with property checking/verification.

Church-Rosser property and intersection types

Abstract Syntax Notation One (ASN.1) is a very popular specification language with many applications in networking. We work towards the correct translation from ASN.1, into the powerful algebraic specification language CafeOBJ. Our aim is to create a software environment that can translate correctly a protocols specification written in ASN.1 into the powerful algebraic specification language CafeOBJ. We believe that such an environment would be a step towards the adoption of algebraic specification methodologies from the networking research community. This formal translation will allow the verification of system-critical properties of the designed protocol at the pre-coding stage of development. The software environment will make full use of the huge ASN.1 specification library and the powerful proving engine of CafeOBJ. In our paper we first introduce the key elements of both ASN.1 and CafeOBJ, and then we sketch our proposed translation rules and suggest a methodology for proving correctness. Finally, as a case study we translate an ASN.1 specification of a basic banking system into CafeOBJ and then use the resulting modules to find and verify some system-critical properties.

Towards a correct translation from ASN.1 into CafeOBJ

Open standardization seems to be very popular among software developers as it simplifies the standard’s adoption by the software engineering. Formal specification methods, while very promising, are being adopted slowly as the industry seems to have little motivation to move into this territory. In this paper the authors present (1) the idea of applying formal specification techniques to open standards’ specifications, and (2) an example of a formal specification of the Rich Site Summary (RSS) v2.0 open standard. The authors provide evidence for the advantages of the open standards formal specification over natural language documentations: formal specifications are more concise, less ambiguous, more complete with respect to the original documentation and, when using certain kinds of specification languages, executable and reusable as they support module inheritance. The merging of formal specification methods and open standards allows (1) a more concrete standard design; (2) an improved understanding of the environment under design; (3) an enforced certain level of precision into the specification, and also (4) provides software engineers with extended property checking/verification capabilities, especially if they opt to use any algebraic specification language. The authors showcase how the RSS standard can be formally specified using an algebraic specification language and demonstrate how can that be beneficial.

Efficient query answering over expressive inconsistent description logics

Query rewriting is an important technique for answering queries over data described using ontologies. In query rewriting the input, a conjunctive query (CQ) q and an ontology O, is transformed into a new datalog query that captures all answers of q over O and any dataset D. This process can be time-consuming as it is of high computational complexity. In many real-world applications, this can be particularly problematic as they involve frequent and relatively small modifications on quite large ontologies. Hence, a drawback of most of modern query rewriting systems is that every time the initial ontology is modified, e.g. when new axioms are added or existing ones removed, they compute a new rewriting from scratch. In this paper, we study the problem of computing a rewriting for a CQ over an ontology that has been modified. We do this by reusing the information obtained by the extraction of some previous rewriting with the goal of performing the least possible computations. We study the problem theoretically, present detailed algorithms for both ontology revision and ontology contraction and finally, present an extensive experimental evaluation using the well-known query rewriting systems Requiem and Rapid.