We investigate properties of convergent and forward-closed string rewriting systems in the context of the syntactic criteria introduced in [8] by Christopher Lynch and Barbara Morawska (we call these LM-Systems). Since a string rewriting system can be viewed as a term-rewriting system over a signature of purely monadic function symbols, we adapt their definition to the string rewriting case. We...

A theorem proving procedure is described which combines the approach of locking resolution with that of rewriting systems. Indeed, both the binary resolution and a complete restr ict ion of paramodulation are embodied by an extension of the rewriting operation called superposition. Experimental results are reported and compared with l i terature automated proofs.

We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete procedure to check nominal algebra equality. This subclass includes specifications of lambda-calculus and first-order ...

We propose an extension of rewriting techniques to derive inclusion relations a ⊆ b between terms built from monotonic operators. Instead of using only a rewriting relation ⊆ −→ and rewriting a to b, we use another rewriting relation ⊇ −→ as well and seek a common expression c such that a ⊆ −→ ∗ c and b ⊇ −→ ∗ c. Each component of the bi-rewriting system 〈 ⊆ −→, ⊇ −→〉 is allowed to be a subset ...

We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete and efficient procedure to check nominal algebra equality. This subclass includes specifications of lambda-calculus an...

We consider the problems of conjunctive query answering and rewriting under Description Logic constraints. We present a query rewriting algorithm for ELHI knowledge bases, and use it to show that query answering in this setting is PTime-complete w.r.t. data complexity. We show that our algorithm is worst-case optimal for languages with data complexity of query answering ranging from LogSpace to...

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to t...

This thesis is primarily concerned with the algebraic semantics of non-terminating term rewriting systems. The usual semantics for rewrite system is based in interpreting rewrite rules as equations and rewriting as a particular case of equational reasoning. The termination of a rewrite system ensures that every term has a value (normal form). But, in general we cannot guarantee this. The resear...

We propose and study a probabilistic logic over an algebraic basis, including equations and domain restrictions. The logic combines aspects from classical logic and equational logic with an exogenous approach to quantitative probabilistic reasoning. We present a sound and weakly complete axiomatization for the logic, parameterized by an equational specification of the algebraic basis coupled wi...

A property is called persistent if for any manysorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that termination is persistent for locally confluent overlay term rewriting systems and we give the example as application of this result. Furthermore we obtain that co...