In this paper we study the completeness of resolution when it is restricted by a non-liftable order and by weak subsumption. A non-liftable order is an order that does not satisfy A ≺ B ⇒ AΘ ≺ BΘ. Clause c1 weakly subsumes c2 if c1Θ ⊆ c2, and Θ is a renaming substitution. We show that it is natural to distinguish 2 types of non-liftable orders and 3 types of weak subsumption, which correspond n...

Currying is a transformation of term rewrite systems which may contain symbols of arbitrary arity into systems which contain only nullary symbols, together with a single binary symbol called application. We show that for all term rewrite systems (whether orthogonal or not) the following properties are preserved by this transformation: strong normalization, weak normalization, weak Church-Rosser...

We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequent-based proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semant...

In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non-unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentzian 3-manifolds with n...

In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentzian 3-manifolds with n...

We show that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non-unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentz 3-manifolds with non compact (local) i...

In this paper we deal with generic expansions of first-order predicate logics of some left-continuous t-norms with a countable set of truth-constants. Besides already known results for the case of Lukasiewicz logic, we obtain new conservativeness and completenesss results for some other expansions. Namely, we prove that the expansions of predicate Product, Gödel and Nilpotent Minimum logics wit...

As it was shown in [7], Monoidal t-norm based logic (MTL) is a logic of left-continuous t-norms. In other words, this means that MTL enjoys the standard completeness theorem. In this paper we present a different proof of this theorem. In fact, we prove even more since we show that MTL is complete w.r.t. the class of standard MTL-algebras with finite congruence lattices or equivalently with fini...

To the Editor: In a recent issue of Circulation, Pappone et al1 report their experience with catheter ablation for atrial fibrillation using long atrial linear lesions. Because they emphasized their difficulty in assessing the completeness of lines, we would like to clear up certain misconceptions concerning this issue. First, the idea that the spatial continuity of marked lesional points indic...