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Preservation of interpolation features by fibring
 Journal of Logic and Computation
"... Fibring is a metalogical constructor that permits to combine different logics by operating on their deductive systems under certain natural restrictions, as for example that the two given logics are presented by deductive systems of the same type. Under such circumstances, fibring will produce a new ..."
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Fibring is a metalogical constructor that permits to combine different logics by operating on their deductive systems under certain natural restrictions, as for example that the two given logics are presented by deductive systems of the same type. Under such circumstances, fibring will produce a new deductive system by means of the free use of inference rules from both deductive systems, provided the rules are schematic, in the sense of using variables that are open for application to formulas with new linguistic symbols (from the point of view of each logic component). Fibring is a generalization of fusion, a less general but wider developed mechanism which permits results of the following kind: if each logic component is decidable (or sound, or complete with respect to a certain semantics) then the resulting logic heirs such a property. The interest for such preservation results for combining logics is evident, and they have been achieved in the more general setting of fibring in several cases. The Craig interpolation property and the Maehara interpolation have a special significance when combining logics, being related to certain problems of complexity theory, some properties of model theory and to the usual (global) metatheorem of deduction. When the peculiarities of the distinction between local and global deduction interfere, justifying what we call careful reasoning, the question of preservation of interpolation becomes more subtle and other forms of interpolation can be distinguished. These questions are investigated and several (global and local) preservation results for interpolation are obtained for fibring logics that fulfill mild requirements. AMS Classification: 03C40, 03B22, 03B45 1
Interpolable Formulas in Equilibrium Logic and Answer Set Programming
"... Interpolation is an important property of classical and many nonclassical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the nonmonotonic system of equilibrium logic, establishing weaker or stronger forms of ..."
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Interpolation is an important property of classical and many nonclassical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the nonmonotonic system of equilibrium logic, establishing weaker or stronger forms of interpolation depending on the precise interpretation of the inference relation. These results also yield a form of interpolation for ground logic programs under the answer sets semantics. For disjunctive logic programs we also study the property of uniform interpolation that is closely related to the concept of variable forgetting. The firstorder version of equilibrium logic has analogous Interpolation properties whenever the collection of equilibrium models is (firstorder) definable. Since this is the case for socalled safe programs and theories, it applies to the usual situations that arise in practical answer set programming. 1.
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.
Restricted Interpolation in Modal Logics
, 14
"... this paper we prove that PB2 implies IPR. Since PB2 does not imply IPD [12], we get that IPD does not follow from IPR ..."
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this paper we prove that PB2 implies IPR. Since PB2 does not imply IPD [12], we get that IPD does not follow from IPR
Interpolation for Predefined Types
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2008
"... ... model theoretic framework of the theory of institutions. For this semantics we develop a generic interpolation result which can be easily applied to various concrete situations from the theory and practice of specification and programming. Our study of interpolation is motivated by a number of i ..."
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... model theoretic framework of the theory of institutions. For this semantics we develop a generic interpolation result which can be easily applied to various concrete situations from the theory and practice of specification and programming. Our study of interpolation is motivated by a number of important applications to computing science especially in the area of structured specifications.
A Semantic Approach to Interpolation
"... 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; al ..."
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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.
Interpolation in Equilibrium Logic and Answer Set Programming: the Propositional Case
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Craig Interpolation in the Presence of Unreliable Connectives
, 2014
"... Arrow and turnstile interpolations are investigated in UCL (introduced in [32]), a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile ..."
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Arrow and turnstile interpolations are investigated in UCL (introduced in [32]), a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.