Intuitionistic De Morgan Verification and Falsification Logics

Norihiro Kamide

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Paper

Intuitionistic De Morgan Verification and Falsification Logics

Topics: Knowledge Representation and Reasoning

In Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, 233-240, 2016 , Rome, Italy

Author: Norihiro Kamide

Affiliation: Teikyo University, Japan

Keyword(s): Paraconsistent Logic, De Morgan Laws, Sequent Calculus, Cut-elimination Theorem, Embedding Theorem.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Knowledge Representation and Reasoning ; Symbolic Systems

Abstract: In this paper, two new logics called intuitionistic De Morgan verification logic DV and intuitionistic De Morgan falsification logic DF are introduced as a Gentzen-type sequent calculus. The logics DV and DF have De Morgan-like laws with respect to implication and co-implication. These laws are analogous to the well-known De Morgan laws with respect to conjunction and disjunction. On the one hand, DV can appropriately represent verification (or justification) of incomplete information, on the other hand DF can appropriately represent falsification (or refutation) of incomplete information. Some theorems for embedding DV into DF and vice versa are shown. The cut-elimination theorems for DV and DF are proved, and DV and DF are also shown to be paraconsistent and decidable.

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Paper citation in several formats:

Kamide, N. (2016). Intuitionistic De Morgan Verification and Falsification Logics. In Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART; ISBN 978-989-758-172-4; ISSN 2184-433X, SciTePress, pages 233-240. DOI: 10.5220/0005629902330240

@conference{icaart16,
author={Norihiro Kamide.},
title={Intuitionistic De Morgan Verification and Falsification Logics},
booktitle={Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART},
year={2016},
pages={233-240},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005629902330240},
isbn={978-989-758-172-4},
issn={2184-433X},
}

TY - CONF

JO - Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART
TI - Intuitionistic De Morgan Verification and Falsification Logics
SN - 978-989-758-172-4
IS - 2184-433X
AU - Kamide, N.
PY - 2016
SP - 233
EP - 240
DO - 10.5220/0005629902330240
PB - SciTePress