An important open question in the semantic Web is the precise relationship between the RDF(S) semantics and the semantics of standard knowledge representation formalisms such as logicprogramming and description logic...
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ISBN:
(纸本)9783540762973
An important open question in the semantic Web is the precise relationship between the RDF(S) semantics and the semantics of standard knowledge representation formalisms such as logicprogramming and description logics. In this paper we address this issue by considering embeddings of RDF and RDFS in logic. Using these embeddings, combined with existing results about various fragments of logic, we establish several novel complexity results. the embeddings we consider show how techniques from deductive databases and description logics can be used for reasoning with RDF(S). Finally, we consider querying RDF graphs and establish the data complexity of conjunctive querying for the various RDF entailment regimes.
We introduce a formal argumentation method based on normal programs and rewriting systems which is able to define extensions of the grounded semantics based on specific rewriting rules which perform particular kind of...
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ISBN:
(纸本)9781607508427;9781607508410
We introduce a formal argumentation method based on normal programs and rewriting systems which is able to define extensions of the grounded semantics based on specific rewriting rules which perform particular kind of reasoning as in reasoning by cases. these new argumentation semantics are intermediate argumentation semantics between the grounded and the preferred semantics.
Focused proofs are sequent calculus proofs that group inference rules into alternating positive and negative phases. these phases can then be used to define macro-level inference rules Gentzen's original and tiny ...
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ISBN:
(数字)9783662488997
ISBN:
(纸本)9783662488997;9783662488980
Focused proofs are sequent calculus proofs that group inference rules into alternating positive and negative phases. these phases can then be used to define macro-level inference rules Gentzen's original and tiny introduction and structural rules. We show here that the inference rules of labeled proof systems for modal logics can similarly be described as pairs of such phases within the LKF focused proof system for first-order classical logic. We consider the system G3K of Negri for the modal logic K and define a translation from labeled modal formulas into first-order polarized formulas and show a strict correspondence between derivations in the two systems, i.e., each rule application in G3K corresponds to a bipole-a pair of a positive and a negative phases-in LKF. Since geometric axioms (when properly polarized) induce bipoles, this strong correspondence holds for all modal logics whose Kripke frames are characterized by geometric properties. We extend these results to present a focused labeled proof system for this same class of modal logics and show its soundness and completeness. the resulting proof system allows one to define a rich set of normal forms of modal logic proofs.
We investigate the computational complexity of spatial logics extended withthe means to represent topological connectedness and restrict the number of connected components. In particular, we show that the connectedne...
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ISBN:
(纸本)9783540894384
We investigate the computational complexity of spatial logics extended withthe means to represent topological connectedness and restrict the number of connected components. In particular, we show that the connectedness constraints can increase complexity from NP to PSPACE, EXPTIME and, if component counting is allowed, to NEXPTIME.
Jerabek showed in 2008 that cuts in propositional-logic deep-inference proofs can be eliminated in quasipolynomial time. the proof is an indirect one relying on a result of Atserias, Galesi and Pudlak about monotone s...
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ISBN:
(纸本)9783642175107
Jerabek showed in 2008 that cuts in propositional-logic deep-inference proofs can be eliminated in quasipolynomial time. the proof is an indirect one relying on a result of Atserias, Galesi and Pudlak about monotone sequent calculus and a correspondence between this system and cut-free deep-inference proofs. In this paper we give a direct proof of Jerabek's result: we give a quasipolynomial-time cut-elimination procedure in propositional-logic deep inference. the main new ingredient is the use of a computational trace of deep-inference proofs called atomic flows, which are both very simple (they trace only structural rules and forget logical rules) and strong enough to faithfully represent the cut-elimination procedure.
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs P and Q and vocabulary V (set of predicates) the existence of a program R in V such that P. R and ...
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ISBN:
(数字)9783031634987
ISBN:
(纸本)9783031634970;9783031634987
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs P and Q and vocabulary V (set of predicates) the existence of a program R in V such that P. R and P. Q are strongly equivalent can be expressed as a first-order entailment. Moreover, our result is effective: A program R can be constructed from a Craig interpolant for this entailment, using a known first-order encoding for testing strong equivalence, which we apply in reverse to extract programs from formulas. As a further perspective, this allows transforming logic programs via transforming their first-order encodings. In a prototypical implementation, the Craig interpolation is performed by first-order provers based on clausal tableaux or resolution calculi. Our work shows how definability and interpolation, which underlie modern logic-based approaches to advanced tasks in knowledge representation, transfer to answer set programming.
the structural semantics of UML-based metamodeling were recently explored[l], providing a characterization of the models adhering to a metamodel. In particular, metamodels can be converted to a set of constraints expr...
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ISBN:
(纸本)9783540752080
the structural semantics of UML-based metamodeling were recently explored[l], providing a characterization of the models adhering to a metamodel. In particular, metamodels can be converted to a set of constraints expressed in a decidable subset of first-order logic, an extended Horn logic. We augment the constructive techniques found in logicprogramming, which are also based on an extended Horn logic, to produce constructive techniques for reasoning about models and metamodels. these methods have a number of practical applications: At the meta-level, it can be decided if a (composite) metamodel characterizes a non-empty set of models, and a member can be automatically constructed. At the model-level, it can be decided if a submodel has an embedding in a well-formed model, and the larger model can be constructed. this amounts to automatic model construction from an incomplete model. We describe the concrete algorithms for constructively solving these problems, and provide concrete examples.
Because of their self-x properties Organic Computing systems are hard to verify. Nevertheless in safety critical domains one may want to give behavioral guarantees. One technique to reduce complexity of the overall ve...
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ISBN:
(纸本)9783642165757
Because of their self-x properties Organic Computing systems are hard to verify. Nevertheless in safety critical domains one may want to give behavioral guarantees. One technique to reduce complexity of the overall verification task is applying composition theorem. In this paper we present a technique for formal specification and compositional verification of Organic Computing systems. Separation of self-x and functional behavior has amongst others, advantages for the formal specification. We present how the specification of self-x behavior can be integrated into an approach for compositional verification of concurrent systems, based on Interval Temporal logic. the presented approach has full tool support withthe KIV interactive theorem prover.
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