306 research outputs found
An interval logic for higher-level temporal reasoning
Prior work explored temporal logics, based on classical modal logics, as a framework for specifying and reasoning about concurrent programs, distributed systems, and communications protocols, and reported on efforts using temporal reasoning primitives to express very high level abstract requirements that a program or system is to satisfy. Based on experience with those primitives, this report describes an Interval Logic that is more suitable for expressing such higher level temporal properties. The report provides a formal semantics for the Interval Logic, and several examples of its use. A description of decision procedures for the logic is also included
The complexity of clausal fragments of LTL
We introduce and investigate a number of fragments of propositional temporal logic LTL over the flow of time (ℤ, <). The fragments are defined in terms of the available temporal operators and the structure of the clausal normal form of the temporal formulas. We determine the computational complexity of the satisfiability problem for each of the fragments, which ranges from NLogSpace to PTime, NP and PSpace
New results on rewrite-based satisfiability procedures
Program analysis and verification require decision procedures to reason on
theories of data structures. Many problems can be reduced to the satisfiability
of sets of ground literals in theory T. If a sound and complete inference
system for first-order logic is guaranteed to terminate on T-satisfiability
problems, any theorem-proving strategy with that system and a fair search plan
is a T-satisfiability procedure. We prove termination of a rewrite-based
first-order engine on the theories of records, integer offsets, integer offsets
modulo and lists. We give a modularity theorem stating sufficient conditions
for termination on a combinations of theories, given termination on each. The
above theories, as well as others, satisfy these conditions. We introduce
several sets of benchmarks on these theories and their combinations, including
both parametric synthetic benchmarks to test scalability, and real-world
problems to test performances on huge sets of literals. We compare the
rewrite-based theorem prover E with the validity checkers CVC and CVC Lite.
Contrary to the folklore that a general-purpose prover cannot compete with
reasoners with built-in theories, the experiments are overall favorable to the
theorem prover, showing that not only the rewriting approach is elegant and
conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page
Autism:Implications for Inclusive Education with respect to Software Engineering
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219448.pdf (preprint version ) (Open Access)CSERC '1
On word problems in equational theories
The Knuth-Bendix procedure for word problems in universal algebra is known to be very effective when it is applicable. However, the procedure will fail if it generates equations which cannot be oriented into rules (i.e. the system is not noetherian), or if it generates infinitely many rules (i.e. the system is not confluent). In 1980 Huet showed that even if the system is not confluent, the Knuth-Bendix procedure still yiels a demi-decision procedure for word problems, provided that every equation can be oriented. In this paper we show that even if there are non-orientable equations, the Knuth-Bendix procedure can still be modified into a reasonably efficient semi-decision procedure for word problems in equational theories. Thus, we have lifted the noetherian requirement in the Knuth-Bendix procedure. Several confluence results are also given in the paper together with some experiments. Our method can also be extended to more general theories. Comparison with related works is also given. The proof of completeness, which is an interesting subject by itself, employs a new proof technique which utilizes a notion of transfinite semantic trees which is designed for proving refutational completeness of theorem proving methods in general
Acute Leriche syndrome due to the thrombus in the left ventricle.
Abstract. In this contribution we present a variant of a resolution theorem prover which selects resolution steps based on the proportion of models a newly generated clause satisfies compared to all models given in a reference class. This reference class is generated from a subset of the initial clause set. Since the empty clause does not satisfy any models, preference is given to such clauses which satisfy few models only. Because computing the number of models is computationally expensive on the one hand, but will remain almost unchanged after the application of one single resolution step on the other hand, we adapt Kowalski’s connection graph method to store the number of models at each link.
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