Simulations of zero-one laws in modal logics GL, S4 and K4

Łucki, Jakub (2022) Simulations of zero-one laws in modal logics GL, S4 and K4. Bachelor's Thesis, Artificial Intelligence.

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Abstract

A zero-one law is a property of modal logics stating that any formula is either almost always valid or almost always invalid in a given modal logic. This property can concern both model validity and frame validity. Furthermore, it has been shown that all modal logics obey zero-one laws concerning model validity. However, in the case of frame validity, only a modal logic GL has been successfully proven to have a zero-one law, while several others, such as modal logics S4 and K4, are only hypothesised to obey it. This study aims to empirically confirm the proof for frames and models in GL, and check whether zero-one laws hold for frames and models of S4 and K4. To accomplish this, each of 8047 distinct formulas was validated in 5000 randomly generated models and 500 randomly generated frames of each modal logic. Kleitman and Rothschild's result about the structure of almost all finite partial orders was used as a base for generating models and frames. The experiment's results suggest that the above-mentioned modal logics obey zero-one laws for both models and frames.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Verbrugge, L.C.
Degree programme:	Artificial Intelligence
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	26 Jul 2022 06:27
Last Modified:	17 Aug 2023 15:24
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/28131

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