2003 Fiscal Year Final Research Report Summary
Formal Ontology based on Temporal Logic
| Project/Area Number |
13610002
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Philosophy
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| Research Institution | Saitama University |
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Principal Investigator |
KACHI Daisuke Saitama University, Faculty of Liberal Arts, Associate Professor, 教養学部, 助教授 (50251145)
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| Project Period (FY) |
2001 – 2003
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| Keywords | partial logic / temporal modal logic / formal ontology / philosophy of time / time travel / temporal becoming / substance ontology / tensed ontology |
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| Research Abstract |
Taking temporal becoming as one of important aspects in reality, this research aimed at two tasks : one is constructing a formal system of temporal logic that can properly deal with ontological inferences related to temporal becoming, and the other is building up, based on that system, an inclusive ontological theory that gives a principal role to temporal becoming.
As for the former, I constructed the system of (propositional) temporal partial logic PS4.3. PS4.3 is a system given by making simple partial logic SPL temporal along with S4.3, which is known as a Diodorean modal logic. Since the Kripke frame that characterizes S4.3 is a dense ordered sequence, there the propositions that express possibility can be interpreted as those that insist on their truth at some present or future moments in a dense linear time. After defining the syntax and semantics of PS4.3, I constructed a tableau proof system and showed its soundness, completeness and decidability.
As for the latter, firstly I built up a system of tensed ontology based on SPL and secondly constructed a system of formal ontology of temporal modality based on PS4.3, in accordance with substance ontology.
Moreover I made investigations about two ontological problems concerning time : the possibility of time travel and the reality of temporal becoming. As for the former, making a distinction between the real past and the unreal future along the history of a substance, I proved that the time travels to the past that may bring about paradoxes are impossible. As for the latter, finding in the occurrence of an event a temporal direction of changing from possibility to necessity and from unreality to reality, I insisted that we should recognize the reality of temporal becoming in such an occurrence.
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