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Inductive Definitions, . . .
, 1992
"... We introduce and illustrate a specification method combining rulebased inductive definitions, wellfounded induction principles, fixedpoint theory and abstract interpretation for general use in computer science. Finite as well as infinite objects can be specified, at various levels of details re ..."
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We introduce and illustrate a specification method combining rulebased inductive definitions, wellfounded induction principles, fixedpoint theory and abstract interpretation for general use in computer science. Finite as well as infinite objects can be specified, at various levels of details
Inductive Definitions in the System Coq Rules and Properties
, 1992
"... In the pure Calculus of Constructions, it is possible to represent data structures and predicates using higherorder quantification. However, this representation is not satisfactory, from the point of view of both the efficiency of the underlying programs and the power of the logical system. For ..."
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Cited by 191 (2 self)
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. For these reasons, the calculus was extended with a primitive notion of inductive definitions [8]. This paper describes the rules for inductive definitions in the system Coq. They are general enough to be seen as one formulation of adding inductive definitions to a typed lambdacalculus. We prove strong
Evolution of Inductive Definitions
"... . In formal verification, inductive definitions of predicates are widely used when we define recursive notions and algorithms. In actual verification, we often introduce a new inductively defined predicate by modifying an existing inductive definition. In such a case, it is usual that there are ..."
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. In formal verification, inductive definitions of predicates are widely used when we define recursive notions and algorithms. In actual verification, we often introduce a new inductively defined predicate by modifying an existing inductive definition. In such a case, it is usual
Functional interpretation and inductive definitions
 Journal of Symbolic Logic
"... Abstract. Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finitetype functionals defined using transfinite recursion on wellfounded trees. 1. ..."
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Cited by 7 (3 self)
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Abstract. Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finitetype functionals defined using transfinite recursion on wellfounded trees. 1.
Causality via Inductive Definitions
"... We propose to treat causal laws as rules of inductive definitions. In the context of formal theories of action, this view of causality leads us to a solution to the frame problem. We obtain essentially the same form of successor state axioms as described in (Reiter 1991) by defining fluents ind ..."
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We propose to treat causal laws as rules of inductive definitions. In the context of formal theories of action, this view of causality leads us to a solution to the frame problem. We obtain essentially the same form of successor state axioms as described in (Reiter 1991) by defining fluents
The Finite Stages of Inductive Definitions
 Logical Foundations of Mathematics, Computer Science and Physics — Kurt Gödel’s Legacy
, 1996
"... . In general, the least fixed point of a positive elementary inductive definition over the Herbrand universe is # 1 1 and has no computational meaning. The finite stages, however, are computable, since validity of equality formulas in the Herbrand universe is decidable. We set up a formal system BI ..."
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Cited by 1 (1 self)
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. In general, the least fixed point of a positive elementary inductive definition over the Herbrand universe is # 1 1 and has no computational meaning. The finite stages, however, are computable, since validity of equality formulas in the Herbrand universe is decidable. We set up a formal system
Extending Classical Logic with Inductive Definitions
, 2000
"... The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming and deductiv ..."
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Cited by 69 (46 self)
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The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming
Integrating inductive definitions in sat
 In Nachum Dershowitz and Andrei Voronokov, editors, LPAR, Lecture
"... Abstract. We investigate techniques for supporting inductive definitions (IDs) in SAT, and report on an implementation, called MidL, of the resulting solver. This solver was first introduced in [11], as a part of a declarative problem solving framework. We go about our investigation by proposing a n ..."
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Cited by 3 (3 self)
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Abstract. We investigate techniques for supporting inductive definitions (IDs) in SAT, and report on an implementation, called MidL, of the resulting solver. This solver was first introduced in [11], as a part of a declarative problem solving framework. We go about our investigation by proposing a
Inductive Definitions in Constraint Programming
"... Constraint programming (CP) and answer set programming (ASP) are two declarative paradigms used to solve combinatorial problems. Many modern solvers for both these paradigms rely on partial or complete Boolean representations of the problem to exploit the extremely efficient techniques that have bee ..."
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bottleneck in traditional ASP solvers that exists due to their inability to handle integer variables efficiently. On the other hand, ASP solvers are more efficient than CP systems on problems that involve inductive definitions, such as reachability in a graph. Besides efficiency, ASP syntax is more natural
Results 1  10
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