## Sorted Unification And The Solution Of Semi-Linear Membership Constraints (1992)

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Uribe92sortedunification,

author = {Tomás Esteban Uribe},

title = {Sorted Unification And The Solution Of Semi-Linear Membership Constraints},

institution = {},

year = {1992}

}

### OpenURL

### Abstract

This thesis describes a new representation for sortal constraints and a unification algorithm for the corresponding constrained terms. Variables range over sets of terms described by systems of set constraints , which can express limited inter-variable dependencies. These sets of terms are more general than regular tree languages, but are still closed under intersection. The new unification algorithm shows sorted unification to be decidable for a broad class of sorted signatures, which we call semi-linear , and, more generally, for sort theories with a least Herbrand model that can be represented using the new constraints. Even though the unification problem in question is NP-hard, the generality of the algorithm may allow for particular efficient implementations for more restricted theories. This unification algorithm can be integrated into any of a variety of deductive systems, resulting in a hybrid substitutional reasoner. As an example, the soundness and completeness of a resolutio...