Hsiang, J., Refutational theorem proving using term rewriting systems, Arti cial Intelligence 25 (1985), pp. 255-300. Home/Search Document Not in Database Summary Related Articles Check |
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Sur La Verification De La Satisfaction Pour La Logique Des.. - Mahfoudh (2003) (Correct)
....# is not valid using a theorem prover. Until the 80 s, interest in SAT was motivated by the possibility of using a SAT solver as the main piece of a theorem prover for first order logic [DP60] Using binary decision diagrams (BDD) Bry92] Other methods including term rewriting [DHJP83, Hsi85] and production systems [Sie87] 3.2 History The history of SAT solvers can be divided into three periods that can be put in parallel with the creation and evolution of computers. Until 1960, SAT solving algorithms were just theoretically described but with no real interest as they could not be ....
J. Hsiang. Refutational theorem proving using term-rewriting systems. Artificial Intelligence, pages 255--300, 1985.
Introducing OBJ - Goguen, Winkler, Meseguer.. (1993) (69 citations) (Correct)
....is an area where term rewriting based systems seem to have an advantage over unification based systems like Prolog. 2.4.6 Propositional Calculus Example This subsection gives a decision procedure for a theory of real interest, the propositional calculus. The procedure is due to Hsiang [92], and makes crucial use of associative commutative rewriting. The OBJ3 code for the object PROPC below evolved from OBJ1 code originally written by David Plaisted [77] It reduces tautologuous propositional formulae, in the usual connectives (and, or, implies, not, xor (exclusive or) and iff) to ....
....true and false (plus the basic true, false valued operators = and ifthenelsefi) while QID provides identifiers that begin with an apostrophe, e.g. a. The module import modes extending and protecting are discussed in Section 3.1 below. The rules in this object have been shown by Hsiang [92] to be Church Rosser and terminating modulo the commutative and associative axioms. obj PROPC is sort Prop . extending TRUTH . protecting QID . subsorts Id Bool Prop . constructors op and : Prop Prop Prop [assoc comm idem idr: true prec 2] op xor : Prop Prop Prop [assoc ....
Jieh Hsiang. Refutational Theorem Proving using Term Rewriting Systems. PhD thesis, University of Illinois at Champaign-Urbana, 1981.
Monitoring Programs using Rewriting - Havelund, Rosu (2001) (8 citations) (Correct)
....The last two equations state that a trace, consisting either of a single event or of several, satisfies an atomic proposition if evaluating that atomic proposition on the event yields true. 2.2. Propositional Calculus A rewriting decision procedure for propositional calculus due to Hsiang [17] is adapted and presented. It provides the usual connectives (and) exclusive or) or) negation) implication) and (equivalence) The procedure reduces tautology formulae to the constant true and all the others to some canonical form modulo associativity and ....
....decision is that its semantics could be in conflict with other logics, for example ones in which conjunctive normal forms are desired. An OBJ3 code for this procedure appeared in [8] Below we give its obvious translation to Maude together with its finite trace semantics, noticing that Hsiang [17] showed that this rewriting system modulo associativity and commutativity is Church Rosser and terminates. The Maude team was probably also inspired by this procedure, since the builtin BOOL module is very similar. fmod PROP CALC is extending LOGICS BASIC . Constructors op : ....
J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. PhD thesis, University of Illinois at Champaign-Urbana, 1981.
Monitoring Java Programs with Java PathExplorer - Havelund, Rosu (2001) (24 citations) (Correct)
....them below. The Maude notation will be introduced on the y as we give the examples. 3.1 Propositional Calculus We begin with the following module for propositional calculus, which is heavily used in JPaX, since most logics are based on it. It implements an ecient procedure due to Hsiang [12] to decide validity of propositions: fmod PROP CALC is ex FORMULA . Constructors op : Formula Formula Formula [assoc comm] op : Formula Formula Formula [assoc comm] vars X Y Z : Formula . var As : AtomState . eq true X = X . eq false X = false . eq false ....
J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. PhD thesis, University of Illinois at Champaign-Urbana, 1981.
Java PathExplorer - A Runtime Verification Tool - Havelund, Rosu (2001) (7 citations) (Correct)
....present the Maude notation in more detail here, but we ll introduce some of it on the fly as we give examples, such as the following one. 3.1. 1 Propositional Calculus The following module for propositional calculus, which is heavily used in JPaX, implements an efficient procedure due to Hsiang [9] to decide validity of propositions: fmod PROP CALC is pr FORMULA . Constructors op : Formula Formula Formula [assoc comm] op : Formula Formula Formula [assoc comm] vars X Y Z : Formula . var As : AtomState . eq true X = X . eq false X = false . eq false X ....
J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. PhD thesis, University of Illinois at Champaign-Urbana, 1981.
Testing Linear Temporal Logic Formulae on Finite Execution Traces - Havelund, Rosu (2001) (4 citations) (Correct)
....is body endfm . The body of a functional module consists of a collection of declarations, of which we are using importing, sorts, subsorts, operations, variables and equations, usually in this order. 2. 2 Propositional Calculus A decision procedure for propositional calculus due to Hsiang [16] is presented. It provides the usual truth constants (true and false) together propositional variables and the usual connectives (and) exclusive or) or) negation) implication) and (equivalence) The procedure reduces tautology formulae to the constant true and ....
....and (equivalence) The procedure reduces tautology formulae to the constant true and all the others to some canonical form modulo associativity and commutativity. An OBJ3 code for this procedure appeared in [8] Below we give its obvious translation to Maude, noticing that Hsiang [16] showed that this rewriting system modulo associativity and commutativity is Church Rosser and terminates. The Maude team was probably also inspired by this procedure, since the builtin BOOL module is very similar. fmod PROPOSITIONAL CALCULUS is protecting QID . sort Formula . subsort Qid ....
Jieh Hsiang. Refutational Theorem Proving using Term Rewriting Systems. PhD thesis, University of Illinois at Champaign-Urbana, 1981.
Definitions by Rewriting in the Calculus of Constructions - Blanqui (2001) (2 citations) (Correct)
...., are all primitive. The rewrite system is primitive, algebraic, strongly normalizing and confluent (this can be automatically proved by CiME [16] Since it is left linear, its combination with fi is confluent [29] Therefore, it is an admissible CAC. But it lacks many other rules [20] which requires rewriting modulo associativity and commutativity, an extension we leave for future work. 5 Conclusion We have defined an extension of the Calculus of Constructions by functions and predicates defined with rewrite rules. The main contributions of our work are the following : ffl ....
J. Hsiang. Refutational theorem proving using termrewriting systems. Artificial Intelligence, 25:255--300, 1985.
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Hsiang, J., Refutational theorem proving using term rewriting systems, Arti cial Intelligence 25 (1985), pp. 255-300.
Definitions by Rewriting in the Calculus of Constructions - Blanqui (2001) (2 citations) (Correct)
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J. Hsiang. Refutational theorem proving using termrewriting systems. Artificial Intelligence, 25:255--300, 1985.
Generating Optimal Linear Temporal Logic Monitors by Coinduction - Sen, Rosu, Agha (2003) (Correct)
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J. Hsiang. Refutational theorem proving using term rewriting systems. Artificial Intelligence, 25, 1985.
Efficient Monitoring of Safety Properties - Havelund, Rosu (2002) (1 citation) (Correct)
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J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. PhD thesis, University of Illinois at Champaign-Urbana, 1981.
Generating Optimal Linear Temporal Logic Monitors by Coinduction - Sen, Rosu, Agha (2003) (Correct)
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J. Hsiang. Refutational theorem proving using term rewriting systems. Artificial Intelligence, 25:255-- 300, 1985.
The complete list of RTA open problems - Date April Summary (Correct)
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Jieh Hsiang. Refutational theorem proving using term-rewriting systems. Arti cial Intelligence, 25:255-300, March 1985.
Monitoring Algorithms for Metric Temporal Logic Specifications - Thati, Rosu (2004) (1 citation) (Correct)
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Jieh Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
Rewriting-based Techniques for Runtime Verification - Rosu, Havelund (1 citation) (Correct)
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J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
Generating Optimal Linear Temporal Logic Monitors by Coinduction - Sen, Rosu, Agha (2004) (Correct)
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J. Hsiang. Refutational theorem proving using term rewriting systems. Artificial Intelligence, 25, 1985.
EAGLE Monitors by Collecting Facts and Generating.. - Barringer, Goldberg.. (2003) (Correct)
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Jieh Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
EAGLE does Space Efficient LTL Monitoring - Barringer, Goldberg, Havelund, Sen (2003) (Correct)
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J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
Rule-Based Runtime Verification - Barringer, Goldberg, Havelund, Sen (2004) (2 citations) (Correct)
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Jieh Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
Rule-Based Runtime Verification - Barringer, Goldberg, Havelund, Sen (2003) (2 citations) (Correct)
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Jieh Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
Invariant-Driven Strategies for Maude - Francisco Duran Manuel (Correct)
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J. Hsiang. Refutational theorem proving using term rewriting systems. Artificial Intelligence, (25):255-- 300, 1985.
Rewriting-based Techniques for Runtime Verification - Rosu, Havelund (1 citation) (Correct)
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J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
EAGLE does Space Efficient LTL Monitoring - Barringer, Goldberg, Havelund, Sen (2003) (Correct)
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J. Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
EAGLE Monitors by Collecting Facts and Generating.. - Barringer, Goldberg.. (2003) (Correct)
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Jieh Hsiang. Refutational Theorem Proving using Term Rewriting Systems. Artificial Intelligence, 25:255--300, 1985.
Generating Optimal Linear Temporal Logic Monitors by Coinduction - Sen, Rosu, Agha (2003) (Correct)
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J. Hsiang. Refutational theorem proving using term rewriting systems. Artificial Intelligence, 25:255-- 300, 1985.
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