Text as tautology: an exploration in inference, transitivity, and logical compression

Rhetorical structure theory (RST) and relational propositions have been shown useful in analyzing texts as expressions in propositional logic. Because these expressions are systematically derived, they may be expected to model discursive reasoning as articulated in the text. If this is the case, it would follow that logical operations performed on the expressions would be reflected in the texts. In this paper the logic of relational propositions is used to demonstrate the applicability of transitive inference to discourse. Starting with a selection of RST analyses from the research literature, analyses of the logic of relational propositions are performed to identify their corresponding logical expressions and within each expression to identify the inference path implicit within the text. By eliminating intermediary relational propositions, transitivity is then used to progressively compress the expression. The resulting compressions are applied to the corresponding texts and their compressed RST analyses. The application of transitive inference to logical expressions results in abridged texts that are intuitively coherent and logically compatible with their originals. This indicates an underlying isomorphism between the inferential structure of logical expressions and discursive coherence, and it confirms that these expressions function as logical models of the text. Potential areas for application include knowledge representation, logic and argumentation, and RST validation.

Logical derivation search with assumption traceability

In this paper authors research the problem of traceability of assumptions in logical derivation. The essence of this task is to trace which assumptions from the available knowledge base of assumptions are necessary to derive a certain conclusion. The paper presents a new derivation procedure for propositional logic, which ensures traceability feature. For the derivable conclusion formula derivation procedure also returns the smallest set of assumptions those are enough to get derivation of the conclusion formula. Verification of the procedure were performed using authors implementation.

Limits of Quantum B-Algebras

Every set with a binary operation satisfying a true statement of propositional logic corresponds to a solution of the quantum Yang-Baxter equation. Quantum B-algebras and L-algebras are closely related to Yang-Baxter equation theory. In this paper, we study the categories with quantum B-algebras with morphisms of exact ones or spectral ones. We guarantee the existences of both direct limits and inverse limits.