A Semantical Analysis of Second-Order Propositional Modal Logic

Authors: Francesco Belardinelli, Wiebe van der Hoek

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Reproducibility Variable Result LLM Response
Research Type Theoretical This paper is aimed as a contribution to the use of formal modal languages in Artificial Intelligence. We introduce a multi-modal version of Second-order Propositional Modal Logic (SOPML), an extension of modal logic with propositional quantification, and illustrate its usefulness as a specification language for knowledge representation as well as temporal and spatial reasoning. Then, we define novel notions of (bi)simulation and prove that these preserve the interpretation of SOPML formulas. Finally, we apply these results to assess the expressive power of SOPML.
Researcher Affiliation Academia F. Belardinelli Laboratoire IBISC Universit e d Evry, France belardinelli@ibisc.fr W. van der Hoek University of Liverpool, UK wiebe@liverpool.ac.uk
Pseudocode No The paper does not contain any pseudocode or algorithm blocks.
Open Source Code No The paper does not provide any information about open-source code for the methodology described.
Open Datasets No The paper is theoretical and does not involve experiments with datasets for training.
Dataset Splits No The paper is theoretical and does not involve experiments with datasets for validation.
Hardware Specification No The paper is theoretical and does not mention any specific hardware used for experiments.
Software Dependencies No The paper is theoretical and does not mention specific software dependencies with version numbers (e.g., Python, PyTorch versions) for its analysis.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameters or system-level training settings.