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.
Recommended Citation
Ge, Michel, "Temporal Reasoning from Common Language: Three Natural Logics" (2026). CUNY Academic Works.
https://academicworks.cuny.edu/hc_sas_etds/1428
