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44
The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabelle is ..."
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Cited by 422 (47 self)
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Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabelle is now based on higherorder logic  a precise and wellunderstood foundation. Examples illustrate use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown sound and complete. Backwards proof is formalized by metareasoning about objectlevel entailment. Higherorder logic has several practical advantages over other metalogics. Many proof techniques are known, such as Huet's higherorder unification procedure. Key words: higherorder logic, higherorder unification, Isabelle, LCF, logical frameworks, metareasoning, natural deduction Contents 1 History and overview 2 2 The metalogic M 4 2.1 Syntax of the metalogic ......................... 4 2.2 ...
Fresh Logic
 Journal of Applied Logic
, 2007
"... Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with resp ..."
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Cited by 183 (21 self)
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Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with respect to metavariables. We present oneandahalfthorder logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of oneandahalfthorder logic derivability, show them equivalent, show that the derivations satisfy cutelimination, and prove correctness of an interpretation of firstorder logic within it. We discuss the technicalities in a wider context as a casestudy for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation
A Logic of ObjectOriented Programs
, 1998
"... We develop a logic for reasoning about objectoriented programs. The logic is for a language with an imperative semantics and aliasing, and accounts for selfreference in objects. It is much like a type system for objects with subtyping, but our specifications go further than types in detailing pre ..."
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Cited by 130 (5 self)
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We develop a logic for reasoning about objectoriented programs. The logic is for a language with an imperative semantics and aliasing, and accounts for selfreference in objects. It is much like a type system for objects with subtyping, but our specifications go further than types in detailing pre and postconditions. We intend the logic as an analogue of Hoare logic for objectoriented programs. Our main technical result is a soundness theorem that relates the logic to a standard operational semantics.
Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 68 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
A Unifying Framework for Integer and Finite Domain Constraint Programming
, 1997
"... We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capab ..."
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Cited by 32 (2 self)
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We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capabilities. We introduce symbolic constraint abstractions into integer programming. Finally, we discuss possible combinations of the two approaches.
The power of paradox: some recent developments in interactive epistemology
 International Journal of Game Theory
, 2007
"... Abstract Paradoxes of gametheoretic reasoning have played an important role in spurring developments in interactive epistemology, the area in game theory that studies the role of the players ’ beliefs, knowledge, etc. This paper describes two such paradoxes – one concerning backward induction, the ..."
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Cited by 25 (2 self)
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Abstract Paradoxes of gametheoretic reasoning have played an important role in spurring developments in interactive epistemology, the area in game theory that studies the role of the players ’ beliefs, knowledge, etc. This paper describes two such paradoxes – one concerning backward induction, the other iterated weak dominance. We start with the basic epistemic condition of “rationality and common belief of rationality ” in a game, describe various ‘refinements ’ of this condition that have been proposed, and explain how these refinements resolve the two paradoxes. We will see that a unified epistemic picture of game theory emerges. We end with some new foundational questions uncovered by the epistemic program. 1
Executing Formal Specifications need not be Harmful
 SOFTWARE ENGINEERING JOURNAL
, 1996
"... We review the various arguments which have been advanced for and against the use of executable specifications. Examples are given of the problems which may arise in applying this technique and of the benefits which may accrue. A case study is reported in which execution is used to validate the p ..."
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Cited by 22 (6 self)
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We review the various arguments which have been advanced for and against the use of executable specifications. Examples are given of the problems which may arise in applying this technique and of the benefits which may accrue. A case study is reported in which execution is used to validate the published specification of a commercially available package. We conclude that there are circumstances when executable specifications can be of high value but that execution must be used together with, and as a supplement to, other methods of validating specifications such as inspection and proof.
Compiling uncertainty away: Solving conformant planning problems using a classical planner (sometimes
 AAAI
, 2006
"... Even under polynomial restrictions on plan length, conformant planning remains a very hard computational problem as plan verification itself can take exponential time. This heavy price cannot be avoided in general although in many cases conformant plans are verifiable efficiently by means of simple ..."
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Cited by 19 (4 self)
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Even under polynomial restrictions on plan length, conformant planning remains a very hard computational problem as plan verification itself can take exponential time. This heavy price cannot be avoided in general although in many cases conformant plans are verifiable efficiently by means of simple forms of disjunctive inference. This raises the question of whether it is possible to identify and use such forms of inference for developing an efficient but incomplete planner capable of solving nontrivial problems quickly. In this work, we show that this is possible by mapping conformant into classical problems that are then solved by an offtheshelf classical planner. The formulation is sound as the classical plans obtained are all conformant, but it is incomplete as the inverse relation does not always hold. The translation accommodates ‘reasoning by cases ’ by means of an ‘splitprotectandmerge’ strategy; namely, atoms L/Xi that represent conditional beliefs ‘if Xi then L ’ are introduced in the classical encoding, that are combined by suitable actions to yield the literal L when the disjunction X1 ∨ · · · ∨ Xn holds and certain invariants in the plan are verified. Empirical results over a wide variety of problems illustrate the power of the approach.
Width parameters beyond treewidth and their applications
 Computer Journal
, 2007
"... Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compare ..."
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Cited by 19 (0 self)
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Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these ‘width ’ parameters in combinatorial structures delivers—besides traditional treewidth and derived dynamic programming schemes—also a number of other useful parameters like branchwidth, rankwidth (cliquewidth) or hypertreewidth. In this contribution, we demonstrate how ‘width ’ parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.