Reasoning Between the Lines: a Logic of Relational Propositions

Andrew Potter

Abstract


This paper describes how Rhetorical Structure Theory (RST) and relational propositions can be used to define a method for rendering and analyzing texts as expressions in propositional logic.  Relational propositions, the implicit assertions that correspond to RST relations, are defined using standard logical operators and rules of inference.  The resulting logical forms are used to construct logical expressions that map to RST tree structures.  The resulting expressions show that inference is pervasive within coherent texts.  To support reasoning over these expressions, a set of rules for negation is defined.  The logical forms and their negation rules can be used to examine the flow of reasoning and the effects of incoherence.  Because there is a correspondence between logical coherence and the functional relationships of RST, an RST analysis that cannot pass the test of logic is indicative either of a problematic analysis or of an incoherent text.  The result is a method for analyzing the logic implicit within discursive reasoning.

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