arXiv subjects

Wijnand van Woerkom

Publications and source records attributed to Wijnand van Woerkom.

3 recordsLinked to original sources

arXiv2025

Defending the Hierarchical Result Models of Precedential Constraint

In recent years, hierarchical case-based-reasoning models of precedential constraint have been proposed. In various papers, Trevor Bench-Capon criticised these models on the grounds that they would give incorrect outcomes in some cases. In particular, the models would not account for the possibility that intermediate factors are established with different strengths by different base-level factors. In this paper we respond to these criticisms for van Woerkom's result-based hierarchical models. We argue that in some examples Bench-Capon seems to interpret intermediate factors as dimensions, and that applying van Woerkom's dimension-based version of the hierarchical result model to these examples avoids Bench-Capon's criticisms.

cs.AI↗

arXiv2024

The Frobenius equivalence and Beck-Chevalley condition for Algebraic Weak Factorisation Systems

If a locally cartesian closed category carries a weak factorisation system, then the left maps are stable under pullback along right maps if and only if the right maps are closed under pushforward along right maps. We refer to this statement as the Frobenius equivalence and in this paper we state and prove an analogical statement for algebraic weak factorisation systems. These algebraic weak factorisation systems are an explicit variant of the more traditional weak factorisation systems in that the factorisation and the lifts are part of the structure of an algebraic weak factorisation system and are not merely required to exist. Our work has been motivated by the categorical semantics of type theory, where the Frobenius equivalence provides a useful tool for constructing dependent function types. We illustrate our ideas using split fibrations of groupoids, which are the backbone of the groupoid model of Hofmann and Streicher.

math.CT↗

arXiv2016

Number representations and term rewriting

In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and termination in binary and decimal term rewriting systems for both append and tree constructor functions. We find that some of these term rewriting systems are not strongly terminating, which we resolve with minor changes to these systems. Moreover, most of the term rewriting systems discussed do not exhibit the confluence property, which seems more difficult to resolve.

cs.LO↗