Relational queries computable in polynomial time
Information and Control
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Proceedings of the eleventh international conference on Logic programming
The expressive powers of the logic programming semantics
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Equality and Domain Closure in First-Order Databases
Journal of the ACM (JACM)
Compiling defeasible inheritance networks to general logic programs
Artificial Intelligence
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Fixpoint semantics for logic programming a survey
Theoretical Computer Science
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
XSB: A System for Effciently Computing WFS
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Inductive Definability and the Situation Calculus
ILPS '97 International Seminar on Logic Databases and the Meaning of Change, Transactions and Change in Logic Databases
Will Deflation Lead to Depletion? On Non-Monotone Fixed Point Inductions
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
ACM Transactions on Computational Logic (TOCL)
Artificial Intelligence
A framework for representing and solving NP search problems
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
A-system: problem solving through abduction
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Reducing inductive definitions to propositional satisfiability
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Expressive power and abstraction in Essence
Constraints
Building a Knowledge Base System for an Integration of Logic Programming and Classical Logic
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
FO(ID) as an Extension of DL with Rules
ESWC 2009 Heraklion Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications
ICLP '09 Proceedings of the 25th International Conference on Logic Programming
A Deductive System for FO(ID) Based on Least Fixpoint Logic
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Cp-logic: A language of causal probabilistic events and its relation to logic programming
Theory and Practice of Logic Programming
Declarative programming of search problems with built-in arithmetic
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Well-founded semantics and the algebraic theory of non-monotone inductive definitions
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Logic programming for knowledge representation
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Game Solution, Epistemic Dynamics and Fixed-Point Logics
Fundamenta Informaticae - Understanding Computers' Intelligence Celebrating the 100th Volume of Fundamenta Informaticae in Honour of Helena Rasiowa
Fo(fd): Extending classical logic with rule-based fixpoint definitions
Theory and Practice of Logic Programming
An approximative inference method for solving ∃¬so satisfiability problems
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
Grounding FO and FO(ID) with bounds
Journal of Artificial Intelligence Research
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
Answer set programming's contributions to classical logic: an analysis of ASP methodology
Logic programming, knowledge representation, and nonmonotonic reasoning
A semantic account for modularity in multi-language modelling of search problems
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Uniform evaluation of nonmonotonic DL-Programs
FoIKS'12 Proceedings of the 7th international conference on Foundations of Information and Knowledge Systems
Connecting first-order ASP and the logic FO(ID) through reducts
Correct Reasoning
Journal of Artificial Intelligence Research
Relational theories with null values and non-herbrand stable models
Theory and Practice of Logic Programming
A general representation and approximate inference algorithm for sensing actions
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
An approximative inference method for solving ∃∀SO satisfiability problems
Journal of Artificial Intelligence Research
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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Well-known principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing induction over well-founded sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inflationary induction has been formalized in FO(IFP), this article formalizes the principle of iterated induction in a new logic for Nonmonotone Inductive Definitions (ID-logic). The semantics of the logic is strongly influenced by the well-founded semantics of logic programming. This article discusses the formalisation of different forms of (non-)monotone induction by the well-founded semantics and illustrates the use of the logic for formalizing mathematical and common-sense knowledge. To model different types of induction found in mathematics, we define several subclasses of definitions, and show that they are correctly formalized by the well-founded semantics. We also present translations into classical first or second order logic. We develop modularity and totality results and demonstrate their use to analyze and simplify complex definitions. We illustrate the use of the logic for temporal reasoning. The logic formally extends Logic Programming, Abductive Logic Programming and Datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions.