Hitoshi Omori

LORI Conference 2021 Conference Paper

A Generalization of Ordered-Pair Semantics

• Hitoshi Omori
• Jonas R. Becker Arenhart

Abstract In this paper, we generalize the ordered-pair semantics advanced by Matthew Clemens for the Logic of Paradox ( LP ) to n -tuple semantics, for each fixed n. Moreover, we show that the resulting semantics can accommodate not only LP, but also classical logic as well as strong Kleene logic depending on the set of designated (or distinguished) values that one chooses. Building on the technical observations, we offer intuitively plausible readings for the semantics, and we also discuss some weaknesses of the original intuitive reading advanced by Clemens.

LORI Conference 2017 Conference Paper

An Extended First-Order Belnap-Dunn Logic with Classical Negation

• Norihiro Kamide
• Hitoshi Omori

Abstract In this paper, we investigate an extended first-order Belnap-Dunn logic with classical negation. We introduce a Gentzen-type sequent calculus FBD+ for this logic and prove theorems for syntactically and semantically embedding FBD+ into a Gentzen-type sequent calculus for first-order classical logic. Moreover, we show the cut-elimination theorem for FBD+ and prove the completeness theorems with respect to both valuation and many-valued semantics for FBD+.

LORI Conference 2017 Conference Paper

Conjunction and Disjunction in Infectious Logics

• Hitoshi Omori
• Damián Szmuc

Abstract In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction.

LORI Conference 2017 Conference Paper

Counterfactuals in Nelson Logic

• Andreas Kapsner
• Hitoshi Omori

Abstract We motivate and develop an extension of Nelson’s constructive logic N3 that adds a counterfactual conditional to the existing setup. After developing the semantics, we will outline how our account will be able to give a nice analysis of natural language counterfactuals. In particular, the account does justice to the intuitions and arguments that have lead Alan Hájek to claim that most conditionals are false, but assertable, without actually forcing us to endorse that rather uncomfortable claim.

LORI Conference 2017 Conference Paper

Sette's Logics, Revisited

• Hitoshi Omori

Abstract One of the simple approaches to paraconsistent logic is in terms of three-valued logics. Assuming the standard behavior with respect to the “classical"values, there are only two possibilities for paraconsistent negation, namely the negation of the Logic of Paradox and the negation of Sette’s logic P \(^1\). From a philosophical perspective, the paraconsistent negation of P \(^1\) is less discussed due to the lack of an intuitive reading of the third value. Based on these, the aim of this paper is to fill in the gap by presenting a semantics for P \(^1\) à la Jaśkowski which sheds some light on the intuitive understanding of Sette’s logic. A variant of P \(^1\) known as I \(^1\) will be also discussed.

FLAP Journal 2016 Journal Article

A Note on Francez' Half-Connexive Formula.

• Hitoshi Omori

The present note examines an unusual formula studied by Nissim Francez. More specifically, a variant of Nelson’s logic is introduced along the lines of the connexive logic C of Heinrich Wansing, and some basic results including soundness and completeness results are observed.

FLAP Journal 2016 Journal Article

A Simple Connexive Extension of the Basic Relevant Logic BD.

• Hitoshi Omori

Motivated by an open problem formulated by Graham Priest and Richard Sylvan related to the basic relevant logic BD, the present note offers a par- tial solution to the problem by making use of an idea suggested by Heinrich Wansing in the context of connexive logic. The note also presents two other non-connexive options that can be regarded as partial solutions to the problem.

FLAP Journal 2016 Journal Article

Editorial Preface.

• Heinrich Wansing
• Hitoshi Omori
• Thomas Macaulay Ferguson

FLAP Journal 2016 Journal Article

More Modal Semantics without Possible Worlds.

• Daniel Skurt
• Hitoshi Omori

In one of his papers, John Kearns developed a semantics without possi- ble worlds for the normal modal logics T, S4, and S5 and even though his work challenged the orthodox view of Kripkean semantics, his work has never been widely recognized. This probably was due to the complexity of his non- deterministic hierarchic semantics. But contemporary developments in the area of non-deterministic semantics make his work most likely understandable for a bigger audience. In this paper we first try to clarify Kearns’ original approach within the context of non-deterministic semantics and give proofs of soundness and completeness with respect to Hilbert style calculi. Then, we simplify some of Kearns results and reveal its problematic aspects. Finally, we generalize the result to cover more modal logics such as K, KD and KTB. Hitoshi Omori was a Postdoctoral Fellow for Research Abroad of the Japan Society for the Promotion of Science (JSPS) at the time of submission, and now he is a Postdoctoral Research Fellow of JSPS. Daniel Skurt was supported by the Ruhr University Research School PLUS, funded by Germany’s Excellence Initiative [DFG GSC 98/3]. We would like to thank Thomas Ferguson, Rohan French, David Ripley, Christian Straßer and Heinrich Wansing for helpful discussions and/or comments on an earlier draft. Furthermore, we would like to thank Uwe Meinel and Michael De for proofreading our English. Finally, we would like to thank the anonymous referees for correcting our mistakes, and pointing out some important points which were missing in our draft.