Algebraic semantics for natural language: some philosophy, some applications

Information processing, when performed by an intelligent agent, draws on a wide array of knowledge sources. Among them are world knowledge, situation knowledge, conceptual knowledge and linguistic knowledge. The focus in this paper will be on the semantic knowledge which is part of the general linguistic competence of any speaker of a natural language (NL).In particular, this knowledge contains ways of organizing the linguistic ontology, i.e. the collection of heterogeneous entities that make up the domain of discourse. The representation language that is proposed here to model this knowledge stresses the structural properties of the ontology. This approach has been persued under the name of algebraic semantics.The paper starts out by explaining the term "algebraic semantics" as it is used in logic. Two senses of "algebraic" are distinguished that are called here "conceptual" and "structural". These two senses of the algebraic method are then applied to NL semantics. The conceptual part is realized by the method of structuring the domains of linguistic ontology in various ways. Thus plural entities are recognized along with mass entities and events. The common outlook here is mereological or lattice-theoretical. Some applications to the study of plurals are given that are to show the usefulness of the algebraic approach. Finally, the ontology of plurals is addressed, and comments are made on some relevant discussion of mereology in recent philosophical work. In sum, it is contended that the algebraic perspective while being of interest in semantics and philosophy proper, also fits both the spirit and the practice of much work that has been done in the Artificial Intelligence (AI) field of knowledge representation.