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What is a Logic?
 J.Y. BEZIAU (ED.), LOGICA UNIVERSALIS, 113–135
, 2006
"... ... model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual ..."
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... model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum
A semantic approach to interpolation.
 of Lecture Notes in Computer Science,
, 2006
"... Abstract Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for firstorder logic. A few of these results nontrivially generalize known interpolation re ..."
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Abstract Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for firstorder logic. A few of these results nontrivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutions and of algebraic specifications, and a CraigRobinson version of these results.
A note on Robinson consistency lemma
, 2006
"... this paper, we propose to make the proof of this result simpler by directly building (i.e. without generating the three chains of elementary morphisms) a model # i with i = 1, 2 such that: 1 ..."
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this paper, we propose to make the proof of this result simpler by directly building (i.e. without generating the three chains of elementary morphisms) a model # i with i = 1, 2 such that: 1
Amalgamation in the Semantics of CASL
"... We present a semantics for architectural specifications in Casl, including an extended static analysis compatible with modeltheoretic requirements. The main obstacle here is the lack of amalgamation for Casl models. To circumvent this problem, we extend the Casl logic by introducing enriched signat ..."
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We present a semantics for architectural specifications in Casl, including an extended static analysis compatible with modeltheoretic requirements. The main obstacle here is the lack of amalgamation for Casl models. To circumvent this problem, we extend the Casl logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor satisfies the amalgamation property as well as its converse, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institutionindependent fashion. Moreover, amalgamation for enriched Casl means that a variety of results for institutions with amalgamation, such as computation of normal forms and theorem proving for structured specifications, can now be used for Casl.