Nontrivial single axiom schemata and their quasi-nontriviality of Leśniewski-Ishimoto's propositional ontology $\bf L_1$
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| Format: | Preprint |
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2024
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| _version_ | 1866912213616295936 |
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| author | Inoué, Takao Miwa, Tadayoshi |
| author_facet | Inoué, Takao Miwa, Tadayoshi |
| contents | On March 8, 1995, was found the following \it nontrivial \rm single axiom-schema characteristic of Leśniewski-Ishimoto's propositional ontology $\bf L_1$ (Inoué, 1995b \cite{inoue16}). $$(\mathrm{A_{M8})} \enspace εab \wedge εcd . \supset . εaa \wedge εcc \wedge (εbc \supset . εad \wedge εba).$$
In this paper, we shall present the progress about the above axiom-schema from 1995. Here we shall give two criteria \it nontiriviality \rm and \it quasi-nontriviality \rm in order to distinguish two axiom schemata. As main results, among others, in §6 - §8, we shall give the simplified axiom schemata ($\rm A_{S1}$), ($\rm A_{S2}$), ($\rm A_{S3N}$) and ($\rm A_{S3Nd}$) based on ($\mathrm{A_{M8}}$), their nontriviality and quasi-nontriviality. In §9 - §11, we shall give a lot of conjectures for nontrivial single axiom schemata for $\bf L_1$. We shall conclude this paper with summary and some remarks in §12. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_07030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nontrivial single axiom schemata and their quasi-nontriviality of Leśniewski-Ishimoto's propositional ontology $\bf L_1$ Inoué, Takao Miwa, Tadayoshi Logic 03B20, 03B60, 03F03, 03A05, 03A99 On March 8, 1995, was found the following \it nontrivial \rm single axiom-schema characteristic of Leśniewski-Ishimoto's propositional ontology $\bf L_1$ (Inoué, 1995b \cite{inoue16}). $$(\mathrm{A_{M8})} \enspace εab \wedge εcd . \supset . εaa \wedge εcc \wedge (εbc \supset . εad \wedge εba).$$ In this paper, we shall present the progress about the above axiom-schema from 1995. Here we shall give two criteria \it nontiriviality \rm and \it quasi-nontriviality \rm in order to distinguish two axiom schemata. As main results, among others, in §6 - §8, we shall give the simplified axiom schemata ($\rm A_{S1}$), ($\rm A_{S2}$), ($\rm A_{S3N}$) and ($\rm A_{S3Nd}$) based on ($\mathrm{A_{M8}}$), their nontriviality and quasi-nontriviality. In §9 - §11, we shall give a lot of conjectures for nontrivial single axiom schemata for $\bf L_1$. We shall conclude this paper with summary and some remarks in §12. |
| title | Nontrivial single axiom schemata and their quasi-nontriviality of Leśniewski-Ishimoto's propositional ontology $\bf L_1$ |
| topic | Logic 03B20, 03B60, 03F03, 03A05, 03A99 |
| url | https://arxiv.org/abs/2402.07030 |