Information and Computation - Special issue: logic and computational complexity
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Automated reformulation of specifications by safe delay of constraints
Artificial Intelligence
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
Expressive power and abstraction in Essence
Constraints
A framework for representing and solving NP search problems
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Grounding for model expansion in k-guarded formulas with inductive definitions
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Guarded open answer set programming with generalized literals
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
On the complexity of model expansion
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
PBINT, a logic for modelling search problems involving arithmetic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Enfragmo: a system for modelling and solving search problems with logic
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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We address the problem of providing a logical formalization of arithmetic in declarative modelling languages for NP search problems. The challenge is to simultaneously allow quantification over an infinite domain such as the natural numbers, provide natural modelling facilities, and control expressive power of the language. To address the problem, we introduce an extension of the model expansion (MX) based framework to finite structures embedded in an infinite secondary structure, together with "double-guarded" logics for representing MX specifications for these structures. The logics also contain multi-set functions (aggregate operations). Our main result is that these logics capture the complexity class NP on "small-cost" arithmetical structures.