Related papers: A Relation Algebra for Term Rewriting: A different…
Moving from the mathematical theory of (abstract) syntax, we develop a general relational theory of symbolic manipulation parametric with respect to, and accounting for, general notions of syntax. We model syntax relying on categorical…
The relationship between Term Graph Rewriting and Term Rewriting is well understood: a single term graph reduction may correspond to several term reductions, due to sharing. It is also known that if term graphs are allowed to contain…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…
In traditional rewriting theory, one studies a set of terms up to a set of rewriting relations. In algebraic rewriting, one instead studies a vector space of terms, up to a vector space of relations. Strikingly, although both theories are…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
We study rewriting systems whose underlying set of terms is equipped with a vector space structure over a given field. We introduce parallel rewriting relations, which are rewriting relations compatible with the vector space structure, as…
This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
In natural language, often multiple entities appear in the same text. However, most previous works in Relation Extraction (RE) limit the scope to identifying the relation between two entities at a time. Such an approach induces a quadratic…
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
The relational data model requires a theory of relations in which tuples are not only many-sorted, but can also have indexes that are not necessarily numerical. In this paper we develop such a theory and define operations on relations that…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
In this paper, we show how to extend the notion of reducibility introduced by Girard for proving the termination of $\beta$-reduction in the polymorphic $\lambda$-calculus, to prove the termination of various kinds of rewrite relations on…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…