Synthetic Logic

Alex J. Djalali

Abstract


The role of inference as it relates to natural language (NL) semantics has oft been neglected. Recently, there has been a move away by some NL semanticists from the heavy machinery of, say, Montagovian-style semantics to a more proof-based approach.

Although researchers tend to study each type of system independently, MacCartney (2009) and MacCartney and Manning (2009) (henceforth M&M) recently developed an algorithmic approach to natural logic that attempts to combine insights from both monotonicity calculi and various syllogistic fragments to derive compositionally the relation between two NL sentences from the relations of their parts.

At the heart of their system, M&M begin with seven intuitive lexical-semantic relations that NL expressions can stand in, e.g., synonymy and antonymy, and then ask the question: if φ stands in some lexical- semantic relation to ψ; and ψ stands in (a possibly different) lexical- semantic relation to θ; what lexical-semantic relation (if any) can be concluded about the relation between φ and θ? This type of reasoning has the familiar shape of a logical inference rule.

However, the logical properties of their join table have not been explored in any real detail. The purpose of this paper is to give M&M’s table a proper logical treatment. As I will show, the table has the underlying form of a syllogistic fragment and relies on a sort of generalized transitive reasoning.


Keywords


semantics; natural logic; inference, monotonicity calculus, syllogism;

Full Text: PDF