## A Functorial Semantics for Multi-Algebras and Partial Algebras, With Applications to Syntax (2000)

Citations: | 15 - 7 self |

### BibTeX

@MISC{Corradini00afunctorial,

author = {Andrea Corradini and Fabio Gadducci},

title = {A Functorial Semantics for Multi-Algebras and Partial Algebras, With Applications to Syntax},

year = {2000}

}

### OpenURL

### Abstract

Multi-algebras allow for the modeling of nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multi-algebras and partial algebras, analogous to the classical presentation of algebras over a signature as cartesian functors from the algebraic theory over to Set. We introduce two dierent notions of theory over a signature, both having a structure weaker than cartesian, and we consider functors from them to Rel or Pfn, the categories of sets and relations or partial functions, respectively. Next we discuss how the functorial presentation provides guidelines for the choice of syntactical notions for a class of algebras, and as an application we argue that the natural generalization of usual terms are \conditioned terms" for partial algebras, and \term graphs" for multi-algebras. Contents 1 Introduction 2 2 A short recap on multi-algebras 4 3...