On logic of paradox

Zuoquan Lin; Wei Li

On logic of paradox

Zuoquan Lin^*
, Wei Li

^*Corresponding author for this work

Shantou University

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

Priest [19] introduced nonmonotonicity into a paraconsistent logic, so-called logic of paradox LP, that yields a solution to the weakness of paraconsistent logic. The resulting logic (of minimal paradox) LP_m is nonmonotonic in the sense that inconsistency is minimal. The problem of proof theory of logic LP_m left open because the base logic LP is paraconsistent so that syntactic formulations of nonmonotonic logic are not available for LP_m, though LP_m is well characterized by minimal semantics. In this paper, we will provide a minimal tableaux as a satisfactory proof theory for LP_m. We first present a signed tableaux for LP. Then minimal tableaux for LP_m is obtained by revising signed tableaux for LP to fit LP_m in which the branches of non-minimally-inconsistent models of the tableaux are eliminated. The soundness and completeness theorems of the tableaux with respect to the semantics of LP and LP_m are proved, respectively.

Original language	English
Pages (from-to)	248-253
Number of pages	6
Journal	Proceedings of The International Symposium on Multiple-Valued Logic
State	Published - 1995
Externally published	Yes
Event	Proceedings of the 1995 25th International Symposium on Multiple-Valued Logic - Bloomington, IN, USA Duration: 23 May 1995 → 25 May 1995

Cite this

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title = "On logic of paradox",

abstract = "Priest [19] introduced nonmonotonicity into a paraconsistent logic, so-called logic of paradox LP, that yields a solution to the weakness of paraconsistent logic. The resulting logic (of minimal paradox) LPm is nonmonotonic in the sense that inconsistency is minimal. The problem of proof theory of logic LPm left open because the base logic LP is paraconsistent so that syntactic formulations of nonmonotonic logic are not available for LPm, though LPm is well characterized by minimal semantics. In this paper, we will provide a minimal tableaux as a satisfactory proof theory for LPm. We first present a signed tableaux for LP. Then minimal tableaux for LPm is obtained by revising signed tableaux for LP to fit LPm in which the branches of non-minimally-inconsistent models of the tableaux are eliminated. The soundness and completeness theorems of the tableaux with respect to the semantics of LP and LPm are proved, respectively.",

author = "Zuoquan Lin and Wei Li",

year = "1995",

language = "英语",

pages = "248--253",

journal = "Proceedings of The International Symposium on Multiple-Valued Logic",

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publisher = "IEEE Computer Society",

note = "Proceedings of the 1995 25th International Symposium on Multiple-Valued Logic ; Conference date: 23-05-1995 Through 25-05-1995",

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AU - Lin, Zuoquan

AU - Li, Wei

PY - 1995

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N2 - Priest [19] introduced nonmonotonicity into a paraconsistent logic, so-called logic of paradox LP, that yields a solution to the weakness of paraconsistent logic. The resulting logic (of minimal paradox) LPm is nonmonotonic in the sense that inconsistency is minimal. The problem of proof theory of logic LPm left open because the base logic LP is paraconsistent so that syntactic formulations of nonmonotonic logic are not available for LPm, though LPm is well characterized by minimal semantics. In this paper, we will provide a minimal tableaux as a satisfactory proof theory for LPm. We first present a signed tableaux for LP. Then minimal tableaux for LPm is obtained by revising signed tableaux for LP to fit LPm in which the branches of non-minimally-inconsistent models of the tableaux are eliminated. The soundness and completeness theorems of the tableaux with respect to the semantics of LP and LPm are proved, respectively.

AB - Priest [19] introduced nonmonotonicity into a paraconsistent logic, so-called logic of paradox LP, that yields a solution to the weakness of paraconsistent logic. The resulting logic (of minimal paradox) LPm is nonmonotonic in the sense that inconsistency is minimal. The problem of proof theory of logic LPm left open because the base logic LP is paraconsistent so that syntactic formulations of nonmonotonic logic are not available for LPm, though LPm is well characterized by minimal semantics. In this paper, we will provide a minimal tableaux as a satisfactory proof theory for LPm. We first present a signed tableaux for LP. Then minimal tableaux for LPm is obtained by revising signed tableaux for LP to fit LPm in which the branches of non-minimally-inconsistent models of the tableaux are eliminated. The soundness and completeness theorems of the tableaux with respect to the semantics of LP and LPm are proved, respectively.

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M3 - 会议文章

AN - SCOPUS:0029217907

SN - 0195-623X

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EP - 253

JO - Proceedings of The International Symposium on Multiple-Valued Logic

JF - Proceedings of The International Symposium on Multiple-Valued Logic

T2 - Proceedings of the 1995 25th International Symposium on Multiple-Valued Logic

Y2 - 23 May 1995 through 25 May 1995

ER -

On logic of paradox

Abstract

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