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# Two methods for checking formulas of temporal logic

Author: Hugh W McGuire Stanford, Calif. : Dept. of Computer Science, Stanford University, ©1995. Report (Stanford University. Computer Science Department), STAN-CS-TR-95-1551. Print book : EnglishView all editions and formats Abstract: "This dissertation presents two methods for determining satisfiability on validity of formulas of Discrete Metric Annotated Linear Temporal Logic. This logic is convenient for representing and verifying properties of reactive and concurrent systems, including software and electronic circuits. The first method presented here is an algorithm for automatically deciding whether any given propositional temporal formula is satisfiable and, if so, reporting a model of the formula. The classical algorithm for this task defines possible states as settings of the truth- values of particular formulas which are relevant to the given formula; possible states are constructed and then linked according to their associated formulas' constraints on temporally adjacent states, and then certain fulfillment-conditions are checked. The new algorithm here efficiently extends that treatment to formulas with temporal operators which refer to the past or are metric (i.e. refer to measured amounts of time). Then, whereas classical proofs of correctness for such algorithms are existential, the proof here is constructive; the proof here shows that for any given formula being checked, any model of the formula is embedded in the graph of possible states, which implies that the algorithm here can find the model. The second method presented in this dissertation is a deduction-calculus for determining the validity of predicate temporal formulas. Previous work on deduction in temporal logic exploits already well-developed techniques of deduction in first-order logic by representing temporal operators via first-order expressions with time reified as quantified expressions of the natural numbers. The new deduction-calculus presented here employs a refined, conservative version of this translation from temporal forms to expressions with time reified. Quantifications are elided, and addition is used instead of classical complicated combinations of comparisons. Ordering conditions on arithmetic expressions can arise, but such are handled automatically via unification and a decision-procedure for Presburger arithmetic. These features make this deduction-calculus very convenient. With deduction rules such as temporal induction, this deduction-calculus is as powerful as other methods. Further deduction- rules such as rewriting are included for additional convenience."  Read more... (not yet rated) 0 with reviews - Be the first.

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## Details

Document Type: Book Hugh W McGuire Find more information about: Hugh W McGuire 34426902 Cover title."June 1995." viii, 144 pages : illustrations ; 28 cm. Report (Stanford University. Computer Science Department), STAN-CS-TR-95-1551. by Hugh W. McGuire.

### Abstract:

Abstract: "This dissertation presents two methods for determining satisfiability on validity of formulas of Discrete Metric Annotated Linear Temporal Logic. This logic is convenient for representing and verifying properties of reactive and concurrent systems, including software and electronic circuits. The first method presented here is an algorithm for automatically deciding whether any given propositional temporal formula is satisfiable and, if so, reporting a model of the formula. The classical algorithm for this task defines possible states as settings of the truth- values of particular formulas which are relevant to the given formula; possible states are constructed and then linked according to their associated formulas' constraints on temporally adjacent states, and then certain fulfillment-conditions are checked. The new algorithm here efficiently extends that treatment to formulas with temporal operators which refer to the past or are metric (i.e. refer to measured amounts of time). Then, whereas classical proofs of correctness for such algorithms are existential, the proof here is constructive; the proof here shows that for any given formula being checked, any model of the formula is embedded in the graph of possible states, which implies that the algorithm here can find the model. The second method presented in this dissertation is a deduction-calculus for determining the validity of predicate temporal formulas. Previous work on deduction in temporal logic exploits already well-developed techniques of deduction in first-order logic by representing temporal operators via first-order expressions with time reified as quantified expressions of the natural numbers. The new deduction-calculus presented here employs a refined, conservative version of this translation from temporal forms to expressions with time reified. Quantifications are elided, and addition is used instead of classical complicated combinations of comparisons. Ordering conditions on arithmetic expressions can arise, but such are handled automatically via unification and a decision-procedure for Presburger arithmetic. These features make this deduction-calculus very convenient. With deduction rules such as temporal induction, this deduction-calculus is as powerful as other methods. Further deduction- rules such as rewriting are included for additional convenience."

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