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On the Expressive Completeness of the Propositional MuCalculus With Respect to Monadic Second Order Logic
, 1996
"... . Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over tran ..."
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Cited by 94 (5 self)
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. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...
Abstraction for falsification
 In Proceedings of Computer Aided Verification (CAV 2005), volume 3576 of LNCS
, 2005
"... Abstract. Abstraction is traditionally used in the process of verification. There, an abstraction of a concrete system is sound if properties of the abstract system also hold in the concrete system. Specifically, if an abstract state a satisfies a property ψ then all the concrete states that corresp ..."
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Cited by 21 (2 self)
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Abstract. Abstraction is traditionally used in the process of verification. There, an abstraction of a concrete system is sound if properties of the abstract system also hold in the concrete system. Specifically, if an abstract state a satisfies a property ψ then all the concrete states that correspond to a satisfy ψ too. Since the ideal goal of proving a system correct involves many obstacles, the primary use of formal methods nowadays is falsification. There, as in testing, the goal is to detect errors, rather than to prove correctness. In the falsification setting, we can say that an abstraction is sound if errors of the abstract system exist also in the concrete system. Specifically, if an abstract state a violates a property ψ, then there exists a concrete state that corresponds to a and violates ψ too. An abstraction that is sound for falsification need not be sound for verification. This suggests that existing frameworks for abstraction for verification may be too restrictive when used for falsification, and that a new framework is needed in order to take advantage of the weaker definition of soundness in the falsification setting. We present such a framework, show that it is indeed stronger (than other abstraction frameworks designed for verification), demonstrate that it can be made even stronger by parameterizing its transitions by predicates, and describe how it can be used for falsification of branchingtime and lineartime temporal properties, as well as for generating testing goals for a concrete system by reasoning about its abstraction. 1
On Bounded Specifications
 In Proc. of the Int. Conference on Logic for Programming and Automated Reasoning (LPAR’01), LNAI
, 2002
"... Bounded model checking methodologies check the correctness of a system with respect to a given specification by examining computations of a bounded length. Results from settheoretic topology imply that sets in are both open and closed (clopen sets) are precisely bounded sets: membership of a ..."
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Cited by 13 (6 self)
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Bounded model checking methodologies check the correctness of a system with respect to a given specification by examining computations of a bounded length. Results from settheoretic topology imply that sets in are both open and closed (clopen sets) are precisely bounded sets: membership of a word in a clopen set can be determined by examining a bounded prefix of it.
Realization of natural language interfaces using lazy functional programming
 ACM Comp. Surv. 38(4) Article
, 2006
"... The construction of natural language interfaces to computers continues to be a major challenge. The need for such interfaces is growing now that speech recognition technology is becoming more readily available, and people cannot speak those computeroriented formal languages that are frequently used ..."
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Cited by 10 (2 self)
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The construction of natural language interfaces to computers continues to be a major challenge. The need for such interfaces is growing now that speech recognition technology is becoming more readily available, and people cannot speak those computeroriented formal languages that are frequently used to interact with computer applications. Much of the research related to the design and implementation of natural language interfaces has involved the use of highlevel declarative programming languages. This is to be expected as the task is extremely difficult, involving syntactic and semantic analysis of potentially ambiguous input. The use of LISP and Prolog in this area is well documented. However, research involving the relatively new lazy functional programming paradigm is less well known. This paper provides a comprehensive survey of that research.
Natural logic for natural language
 Lecture Notes in Computer Science, Volume 4363
, 2007
"... Abstract. For a cognitive account of reasoning it is useful to factor out the syntactic aspect — the aspect that has to do with pattern matching and simple substitution — from the rest. The calculus of monotonicity, alias the calculus of natural logic, does precisely this, for it is a calculus of ap ..."
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Cited by 6 (0 self)
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Abstract. For a cognitive account of reasoning it is useful to factor out the syntactic aspect — the aspect that has to do with pattern matching and simple substitution — from the rest. The calculus of monotonicity, alias the calculus of natural logic, does precisely this, for it is a calculus of appropriate substitutions at marked positions in syntactic structures. We first introduce the semantic and the syntactic sides of monotonicity reasoning or ‘natural logic’, and propose an improvement to the syntactic monotonicity calculus, in the form of an improved algorithm for monotonicity marking. Next, we focus on the role of monotonicity in syllogistic reasoning. In particular, we show how the syllogistic inference rules (for traditional syllogistics, but also for a broader class of quantifiers) can be decomposed in a monotonicity component, an argument swap component, and an existential import component. Finally, we connect the decomposition of syllogistics to the doctrine of distribution. 1
Realization of NaturalLanguage Interfaces Using Lazy Functional Programming
 ACM Comput. Surv
"... The construction of naturallanguage interfaces to computers continues to be a major challenge. The need for such interfaces is growing now that speechrecognition technology is becoming morereadily available, and people cannot speak those computeroriented formal languages that are frequently used ..."
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Cited by 1 (1 self)
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The construction of naturallanguage interfaces to computers continues to be a major challenge. The need for such interfaces is growing now that speechrecognition technology is becoming morereadily available, and people cannot speak those computeroriented formal languages that are frequently used to interact with computer applications. Much of the research related to the design and implementation of naturallanguage interfaces has involved the use of highlevel declarative programming languages. This is to be expected as the task is extremely difficult, involving syntactic and semantic analysis of potentiallyambiguous input. The use of LISP and Prolog in this area is well documented. However, research involving the relativelynew lazy functionalprogramming paradigm is less well known. This paper provides a comprehensive survey of that research.
2 \ 2 AFMC
, 2003
"... The calculus is an expressive specification language in which modal logic is extended with fixpoint operators, subsuming many dynamic, temporal, and description logics. Formulas of calculus are classified according to their alternation depth, which is the maximal length of a chain of nested alt ..."
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The calculus is an expressive specification language in which modal logic is extended with fixpoint operators, subsuming many dynamic, temporal, and description logics. Formulas of calculus are classified according to their alternation depth, which is the maximal length of a chain of nested alternating least and greatest fixpoint operators. Alternation depth is the major factor in the complexity of calculus modelchecking algorithms. A refined classification of calculus formulas distinguishes between formulas in which the outermost fixpoint operator in the nested chain is a least fixpoint operator ( i formulas, where i is the alternation depth) and formulas where it is a greatest fixpoint operator ( i formulas). The alternationfree calculus (AFMC) consists of calculus formulas with no alternation between least and greatest fixpoint operators. Thus, AFMC is a natural closure of 1 [ 1 , which is contained in both 2 and 2 . In this work we show that 2 \ 2 AFMC. In other words, if we can express a property both as a least fixpoint nested inside a greatest fixpoint and as a greatest fixpoint nested inside a least fixpoint, then we can express also with no alternation between greatest and least fixpoints. Our result refers to calculus over arbitrary Kripke structures. A similar result, for directed calculus formulas interpreted over trees with a fixed finite branching degree, follows from results by Arnold and Niwinski. Their proofs there cannot be easily extended to Kripke structures, and our extension involves symmetric nondeterministic B uchi tree automata, and new constructions for them.
... Afmc
"... The calculus is an expressive specification language in which modal logic is extended with fixpoint operators, subsuming many dynamic, temporal, and description logics. Formulas of calculus are classified according to their alternation depth, which is the maximal length of a chain of nested alt ..."
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The calculus is an expressive specification language in which modal logic is extended with fixpoint operators, subsuming many dynamic, temporal, and description logics. Formulas of calculus are classified according to their alternation depth, which is the maximal length of a chain of nested alternating least and greatest fixpoint operators. Alternation depth is the major factor in the complexity of calculus modelchecking algorithms. A refined classification of calculus formulas distinguishes between formulas in which the outermost fixpoint operator in the nested chain is a least fixpoint operator ( i formulas, where i is the alternation depth) and formulas where it is a greatest fixpoint operator ( i formulas). The alternationfree calculus (AFMC) consists of calculus formulas with no alternation between least and greatest fixpoint operators. Thus, AFMC is a natural closure of 1 [ 1 , which is contained in both 2 and 2 . In this work we show that 2 \ 2 AFMC. In other words, if we can express a property both as a least fixpoint nested inside a greatest fixpoint and as a greatest fixpoint nested inside a least fixpoint, then we can express also with no alternation between greatest and least fixpoints. Our result refers to calculus over arbitrary Kripke structures. A similar result, for directed calculus formulas interpreted over trees with a fixed finite branching degree, follows from results by Arnold and Niwinski. Their proofs there cannot be easily extended to Kripke structures, and our extension involves symmetric nondeterministic Buchi tree automata, and new constructions for them.
unknown title
"... Abstract. The �calculus is an expressive specification language in which modal logic is extended with fixpoint operators, subsuming many dynamic, temporal, and description logics. Formulas of �calculus are classified according to their alternation depth, which is the maximal length of a chain of n ..."
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Abstract. The �calculus is an expressive specification language in which modal logic is extended with fixpoint operators, subsuming many dynamic, temporal, and description logics. Formulas of �calculus are classified according to their alternation depth, which is the maximal length of a chain of nested alternating least and greatest fixpoint operators. Alternation depth is the major factor in the complexity of �calculus modelchecking algorithms. A refined classification of �calculus formulas distinguishes between formulas in which the outermost fixpoint operator in the nested chain is a least fixpoint operator formulas, where � is the alternation depth) and formulas where it is a greatest fixpoint operator (��� formulas). The alternationfree �calculus (AFMC) consists of �calculus formulas with no alternation between least and greatest fixpoint operators. Thus, AFMC is a natural closure � �� � � � of, which is contained both � � and � � in. In this work we that � �� � � �� � show AFMC. In other words, if we can express property � a both as a least fixpoint nested inside a greatest fixpoint and as a greatest fixpoint nested inside a least fixpoint, then we express � can also with no alternation between greatest and least fixpoints. Our result to � referscalculus over arbitrary Kripke structures. A similar result, for directedcalculus formulas interpreted over trees with a fixed finite branching degree, follows from results by Arnold and Niwinski. Their proofs there cannot be easily extended to Kripke structures, and our extension involves symmetric nondeterministic Büchi tree automata, and new constructions for them.