Papers by Viorica Sofronie-Stokkermans
Scientific Annals of Computer Science, 2013
In this paper we show that subsumption problems in the description logics EL and EL + can be expr... more In this paper we show that subsumption problems in the description logics EL and EL + can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras, to obtain uniform PTIME decision procedures for TBox and CBox subsumption in EL and EL + . These locality considerations allow us to present a new family of (possibly many-sorted) logics which extend EL and EL + with n-ary roles and/or numerical domains.
The paper presents a modular superposition calculus for the combination of first-order theories i... more The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. Modularity means that inferences are pure, only involving clauses over the alphabet of either one, but not both, of the theories. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combined theory does not depend on the totality of the functions in the extensions, the inconsistency will be effectively found. Moreover, we consider a constraint superposition calculus for the case of hierarchical theories and show that it has a related modularity property. Finally we identify cases where the partial models can always be made total so that modular superposition is also complete with respect to the standard (total function) semantics of the theories.
All in-text references underlined in blue are linked to publications on ResearchGate, letting you... more All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Lecture Notes in Computer Science, 2002
In this paper we analyze some fragments of the universal theory of distributive lattices with man... more In this paper we analyze some fragments of the universal theory of distributive lattices with many sorted bridging operators. Our interest in such algebras is motivated by the fact that, in description logics, numerical features are often expressed by using maps that associate numerical values to sets (more generally, to lattice elements). We first establish a link between satisfiability of universal sentences with respect to algebraic models and satisfiability with respect to certain classes of relational structures. We use these results for giving a method for translation to clause form of universal sentences, and provide some decidability results based on the use of resolution or hyperresolution. Links between hyperresolution and tableau methods are also discussed, and a tableau procedure for checking satisfiability of formulae of type t1 ≤ t2 is obtained by using a hyperresolution calculus.
Studies in Fuzziness and Soft Computing, 2003
Abstract: We give a uniform presentation of representation and decidabilityresults related to the... more Abstract: We give a uniform presentation of representation and decidabilityresults related to the Kripke-style semantics of several nonclassicallogics. We show that a general representation theorem (whichhas as particular instances the representation theorems as algebras ofsets for Boolean algebras, distributive lattices and semilattices) extendsin a natural way to several classes of operators and allows to establisha relationship between algebraic and Kripke-style
2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2014
Theories -numbers -polynomials -functions over numeric domains -algebras Tasks -construct proofs ... more Theories -numbers -polynomials -functions over numeric domains -algebras Tasks -construct proofs -check proofs MATHEMATICS • Theories from mathematical analysis Functions over R -monotone, bounded -continuous, differentiable
Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329)
In this paper we present a method for automated theorem proving in non-classical logics having as... more In this paper we present a method for automated theorem proving in non-classical logics having as algebraic models bounded distributive lattices with certain types of operators. The idea is to use a Priestley-style representation for distributive lattices with operators in order to define a class of Kripke-style models with respect to which the logic is sound and complete. If this class of Kripke-style models is elementary, it can then be used for a translation to clause form; satisfiability of the resulting clauses can be checked by resolution. We illustrate the ideas by several examples.
Proceedings 31st IEEE International Symposium on Multiple-Valued Logic
Scientific Annals of Computer Science, 2013
In this paper we show that subsumption problems in lightweight description logics (such as E L an... more In this paper we show that subsumption problems in lightweight description logics (such as E L and E L + ) can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras, to obtain uniform PTIME decision procedures for CBox subsumption in E L , E L + and extensions thereof. These locality considerations allow us to present a new family of (possibly many-sorted
In this paper we present an overview of results that show that states, transitions and behavior o... more In this paper we present an overview of results that show that states, transitions and behavior of concurrent systems can often be modeled as sheaves over a suitable topological space. In such contexts, geometric logic can be used to test whether (and describe which) local properties, of individual systems, are preserved, at a global level, when interconnecting the systems
1 Resume of the Development of the Scenarios After compiling an exhaustive list of contemporary r... more 1 Resume of the Development of the Scenarios After compiling an exhaustive list of contemporary relevant problems in robotics (cf. Wan90]) and adapting them to make them amenable for approaches based on logic, the RISC-MEDLAR group suggested some rst toy examples in PSW90]. These were primarily meant to demonstrate principles and possible approaches in the area of robotics. One of those examples, involving car painting, will be used (in slightly adapted form) in the current demonstrator work package. It consisted of a working space with four cells and two corridors containing eighty cars that were to be painted by three robots. Their actions were subject to certain restrictions on the number of cars to be painted in a given colour and the suitability of certain cells for painting or moving tasks. The second example dealt with seven robots, three responsible for assembling bicycles and four charged with moving certain necessary parts to the assembly robots. Other parts were to be taken from a conveyor belt. A full description of both scenarios can be found in PSW90]. These examples were meant to provoke thought on the task MEDLAR had to set itself in the demonstration of the practical reasoning approach, and the adaptation of one of these two examples for the nal demonstrator (cf. CCK + 95]) illustrates their success. Thanks to feedback from partners from engineering and industry (about which more in a later section), we got a clearer picture of the state of the art problems in production planning and automation for robot scenarios and areas like CIM. This led us to set up a database for scenario construction, cf. DPSS91], which we used to compose robotics scenarios of industrial relevance that we tried to model
Lecture Notes in Computer Science, 2013
In this paper we study possibilities of efficient reasoning in combinations of theories over poss... more In this paper we study possibilities of efficient reasoning in combinations of theories over possibly non-disjoint signatures. We first present a class of theory extensions (called local extensions) in which hierarchical reasoning is possible, and give several examples from computer science and mathematics in which such extensions occur in a natural way. We then identify situations in which combinations of local extensions of a theory are again local extensions of that theory. We thus obtain criteria both for recognizing wider classes of local theory extensions, and for modular reasoning in combinations of theories over non-disjoint signatures.
Advances in Modal Logic, 2008
We show that subsumption problems in EL and related description logics can be expressed as unifor... more We show that subsumption problems in EL and related description logics can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras to obtain uniform PTIME decision procedures for CBox subsumption in EL and extensions thereof. These locality considerations allow us to present a new family of logics which extend EL and EL + with n-ary roles and/or numerical domains. Definition 1. Let C be a CBox, and C 1 , C 2 two concept descriptions. Then C 1 C C 2 if and only if C I 1 ⊆C I 2 for every model I of C.
Description Logics, 2020
We address the problem of finding high-level explanations for concept subsumption w.r.t. combinat... more We address the problem of finding high-level explanations for concept subsumption w.r.t. combinations of EL (resp. EL) CBoxes. Our goal is to find explanations for concept subsumptions in such combinations of CBoxes which contain only symbols (concept names and role names) that are common to the CBoxes. For this, we use the encoding of TBox subsumption as a uniform word problem in classes of semilattices with monotone operators for EL and the ≤-interpolation property in these classes of algebras, as well as extensions to these results in the presence of role inclusions. For computing the ≤-interpolating terms we use a translation to propositional logic and methods for computing Craig interpolants in propositional logic.
arXiv (Cornell University), Jul 17, 2023
We study the problem of P-interpolation, where P is a set of binary predicate symbols, for certai... more We study the problem of P-interpolation, where P is a set of binary predicate symbols, for certain classes of local extensions of a base theory. For computing the P-interpolating terms, we use a hierarchic approach: This allows us to compute the interpolating terms using a method for computing interpolating terms in the base theory. We use these results for proving ≤-interpolation in classes of semilattices with monotone operators; we show, by giving a counterexample, that ≤-interpolation does not hold if by "shared" symbols we mean just the common symbols. We use these results for the study of ⊑-interpolation in the description logics E L and E L + .
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Papers by Viorica Sofronie-Stokkermans