Date of Award

Fall 1-2-2026

Document Type

Thesis

Degree Name

Master of Arts (MA)

Department

Computer Science

First Advisor

Subash Shankar

Second Advisor

Yuna Won

Third Advisor

Saadeddine Mneimneh

Academic Program Adviser

Subash Shankar

Abstract

This work extends the syllogistic natural logic A developed by Larry Moss -- a language with only sentences of the form "All p are q" -- to account for the simple past and simple future tenses of "to be," developing sound, complete, and efficiently decidable proof systems for the fragments of English with sentences {"All p are q", "All p were q"}, {"All p are q", "All p will be q"}, and {"All p are q", "All p were q", "All p will be q"}. The proposed natural logic system introduces a model theoretic semantics with a discrete, linear, and two-way infinite model of time, which serves as a foundational model that can be adapted in future research. A semantic analysis of "All p were q" and "All p will be q" leads to the conclusion that the "universal" interpretation, in which sentences apply to every moment on the whole timeline, is both natural to common usage and the most suitable for the development of non-trivial syllogistic logic systems. Completeness proofs are done by canonical model for the past- and future-only fragments and by contrapositive for the full version with both tenses. This research contributes three novel, foundational syllogistic systems that account for the passage of time, establishing a basic hierarchy of temporal natural logics with corresponding proof techniques, and proposes several dimensions along which the settings of the logic can be adjusted for future development of alternative or more complex temporal natural logics.

Available for download on Friday, June 25, 2027

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