Termination orderings for associative-commutative rewriting systems

In this paper we describe a new class of orderings—associative path orderings—for proving termination of associative-commutative term rewriting systems .These orderings are based on the concept of simplification orderings and extend the well-known recursive path orderings to E - congruence classes, where E is an equational theory consisting of associativity and commutativity axioms. Associative path orderings are applicable to term rewriting systems for which a precedence ordering on the set of operator symbols can be defined that satisfies a certain condition,the associative path condition. The precedence ordering can often be derived from the structure of the reduction rules. We include termination proofs for various term rewriting systems (for rings,boolean algebra,etc.) and, in addition, point out ways to handle situations where the associative path condition is too restrictive

Ordering constraints on trees

We survey recent results about ordering constraints on trees and discuss their applications. Our main interest lies in the family of recursive path orderings which enjoy the properties of being total, well-founded and compatible with the tree constructors. The paper includes some new results, in particular the undecidability of the theory of lexicographic path orderings in case of a non-unary signature

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

Abstract Canonical Inference

An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) "fairness," which yields completeness, and "uniform fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi

Automated deduction with built-in theories: completeness results and constraint solving techniques

Postprint (published version

Applications and extensions of context-sensitive rewriting

[EN] Context-sensitive rewriting is a restriction of term rewriting which is obtained by imposing replacement restrictions on the arguments of function symbols. It has proven useful to analyze computational properties of programs written in sophisticated rewriting-based programming languages such asCafeOBJ, Haskell, Maude, OBJ*, etc. Also, a number of extensions(e.g., to conditional rewritingor constrained equational systems) and generalizations(e.g., controlled rewritingor forbidden patterns) of context-sensitive rewriting have been proposed. In this paper, we provide an overview of these applications and related issues. (C) 2021 Elsevier Inc. All rights reserved.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Applications and extensions of context-sensitive rewriting. Journal of Logical and Algebraic Methods in Programming. 121:1-33. https://doi.org/10.1016/j.jlamp.2021.10068013312

Deontic Logic and Natural Language

There has been a recent surge of work on deontic modality within philosophy of language. This work has put the deontic logic tradition in contact with natural language semantics, resulting in significant increase in sophistication on both ends. This chapter surveys the main motivations, achievements, and prospects of this work

Cross-categorial gradability in Logoori

The central empirical observation of this paper is that there are polysemous lexical items in a number of unrelated languages that have similar, not intuitively related, meanings. These meanings are 'to arrive'/'to reach,' 'to be enough,' and 'must.' The central theoretical claim of this paper is based on a case study of one such polysemous lexical item in Logoori (Bantu, JE 41; Kenya). We argue that these three meanings all arise from a single semantic denotation that is sensitive to a shared gradable component in the semantics of linguistic expressions referring to spatial paths, gradable predicates, measures of plural count nouns/mass nouns, and modals. The main theoretical issue addressed in this paper is the application of ordered, abstract scales in a model of grammar. This paper is an abridged version of Bowler & Gluckman, to appear