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18
ModelTheoretic Methods in Combined Constraint Satisfiability
 Journal of Automated Reasoning
, 2004
"... We extend NelsonOppen combination procedure to the case of theories which are compatible with respect to a common subtheory in the shared signature. The notion of compatibility relies on model completions and related concepts from classical model theory. ..."
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We extend NelsonOppen combination procedure to the case of theories which are compatible with respect to a common subtheory in the shared signature. The notion of compatibility relies on model completions and related concepts from classical model theory.
Connecting ManySorted Theories’, The
 Journal of Symbolic Logic
, 2007
"... Abstract. Basically, the connection of two manysorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of ..."
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Cited by 24 (7 self)
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Abstract. Basically, the connection of two manysorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the socalled Econnection approach for combining modal logics to an algebraic setting. §1. Introduction. The combination of decision procedures for logical theories arises in many areas of logic in computer science, such as constraint solving, automated deduction, term rewriting, modal logics, and description logics. In general, one has two firstorder theories T1 and T2 over signatures Σ1 and Σ2, for which validity of a certain type of formulae (e.g., universal, existential positive,
Combining decision procedures for the reals
 In preparation
"... Vol. 2 (4:4) 2006, pp. 1–42 www.lmcsonline.org ..."
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Connecting manysorted structures and theories through adjoint functions
 In Proc. 5th FroCoS
, 2005
"... functions ..."
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Rewritingbased Quantifierfree Interpolation for a Theory of Arrays
"... The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifierfree interpolants in general. In th ..."
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Cited by 6 (2 self)
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The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifierfree interpolants in general. In this paper, we show that, with a minor extension to the theory of arrays, it is possible to obtain quantifierfree interpolants. We prove this by designing an interpolating procedure, based on solving equations between array updates. Rewriting techniques are used in the key steps of the solver and its proof of correctness. To the best of our knowledge, this is the first successful attempt of computing quantifierfree interpolants for a theory of arrays. Digital Object Identifier 10.4230/LIPIcs.RTA.2011.171
On the Fusion of coalgebraic logics
"... Abstract. Fusion is arguably the simplest way to combine modal logics. For normal modal logics with Kripke semantics, many properties such as completeness and decidability are known to transfer from the component logics to their fusion. In this paper we investigate to what extent these results can b ..."
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Abstract. Fusion is arguably the simplest way to combine modal logics. For normal modal logics with Kripke semantics, many properties such as completeness and decidability are known to transfer from the component logics to their fusion. In this paper we investigate to what extent these results can be generalised to the case of arbitrary coalgebraic logics. Our main result generalises a construction of Kracht and Wolter and confirms that completeness transfers to fusion for a large class of logics over coalgebraic semantics. This result is independent of the rank of the logics and relies on generalising the notions of distance and box operator to coalgebraic models. 1
Parallel composition of logic calculi with proofs as generalized 2cells
 Preprint, SQIG  IT and IST  TU Lisbon
, 2010
"... Recent graphtheoretic developments [26, 27] in the semantic theory of combination of logics look at a signature as a multigraph (of sorts and connectives) and obtain the induced language as the category of multipaths where formulas appear as morphisms. This idea is carried over to Hilbertstyle de ..."
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Recent graphtheoretic developments [26, 27] in the semantic theory of combination of logics look at a signature as a multigraph (of sorts and connectives) and obtain the induced language as the category of multipaths where formulas appear as morphisms. This idea is carried over to Hilbertstyle deductive systems by looking at an inference rule as a metaedge from its premises to its conclusion. From such a deductive system, a generalized 2category is induced where proofs appear as 2cells. Vertical composition is used for concatenating proofs and horizontal composition for instantiation. The workabilityofthe approachis illustrated by defining freeandsynchronizedvariantsofparallelcompositionofdeductivesystems and proving the conservative nature of the free variant.
On the Multimodal Logic of Normative Systems
"... Abstract. We introduce Multimodal Logics of Normative Systems as a contribution to the development of a general logical framework for reasoning about normative systems over logics for MultiAgent Systems. Given a multimodal logic L, for every modality ✷i and normative system η, we expand the languag ..."
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Abstract. We introduce Multimodal Logics of Normative Systems as a contribution to the development of a general logical framework for reasoning about normative systems over logics for MultiAgent Systems. Given a multimodal logic L, for every modality ✷i and normative system η, we expand the language adding a new modality ✷ η i with the intended meaning of ✷ηi φ being ”φ is obligatory in the context of the normative system η over the logic L”. In this expanded language we define the Multimodal Logic of Normative Systems over L, for any given set of normative systems N, and we give a sound and complete axiomatisation for this logic, proving transfer and model checking results. The special case when L and N are axiomatised by sets of Sahlqvist or shallow modal formulas is studied.