Proof Theory of Finite-valued Logics

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics

A Semantic Similarity Measure for Expressive Description Logics

A totally semantic measure is presented which is able to calculate a similarity value between concept descriptions and also between concept description and individual or between individuals expressed in an expressive description logic. It is applicable on symbolic descriptions although it uses a numeric approach for the calculus. Considering that Description Logics stand as the theoretic framework for the ontological knowledge representation and reasoning, the proposed measure can be effectively used for agglomerative and divisional clustering task applied to the semantic web domain.Comment: 13 pages, Appeared at CILC 2005, Convegno Italiano di Logica Computazionale also available at http://www.disp.uniroma2.it/CILC2005/downloads/papers/15.dAmato_CILC05.pd

Tractable approximate deduction for OWL

Acknowledgements This work has been partially supported by the European project Marrying Ontologies and Software Technologies (EU ICT2008-216691), the European project Knowledge Driven Data Exploitation (EU FP7/IAPP2011-286348), the UK EPSRC project WhatIf (EP/J014354/1). The authors thank Prof. Ian Horrocks and Dr. Giorgos Stoilos for their helpful discussion on role subsumptions. The authors thank Rafael S. Gonçalves et al. for providing their hotspots ontologies. The authors also thank BoC-group for providing their ADOxx Metamodelling ontologies.Peer reviewedPostprin

Heap Abstractions for Static Analysis

Heap data is potentially unbounded and seemingly arbitrary. As a consequence, unlike stack and static memory, heap memory cannot be abstracted directly in terms of a fixed set of source variable names appearing in the program being analysed. This makes it an interesting topic of study and there is an abundance of literature employing heap abstractions. Although most studies have addressed similar concerns, their formulations and formalisms often seem dissimilar and some times even unrelated. Thus, the insights gained in one description of heap abstraction may not directly carry over to some other description. This survey is a result of our quest for a unifying theme in the existing descriptions of heap abstractions. In particular, our interest lies in the abstractions and not in the algorithms that construct them. In our search of a unified theme, we view a heap abstraction as consisting of two features: a heap model to represent the heap memory and a summarization technique for bounding the heap representation. We classify the models as storeless, store based, and hybrid. We describe various summarization techniques based on k-limiting, allocation sites, patterns, variables, other generic instrumentation predicates, and higher-order logics. This approach allows us to compare the insights of a large number of seemingly dissimilar heap abstractions and also paves way for creating new abstractions by mix-and-match of models and summarization techniques.Comment: 49 pages, 20 figure

Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram