• Title/Summary/Keyword: (Substructural) Fuzzy logic

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Set-theoretic Kripke-style Semantics for Weakly Associative Substructural Fuzzy Logics (약한 결합 원리를 갖는 준구조 퍼지 논리를 위한 집합 이론적 크립키형 의미론)

  • Yang, Eunsuk
    • Korean Journal of Logic
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    • v.22 no.1
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    • pp.25-42
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    • 2019
  • This paper deals with Kripke-style semantics, which will be called set-theoretic Kripke-style semantics, for weakly associative substructural fuzzy logics. We first recall three weakly associative substructural fuzzy logic systems and then introduce their corresponding Kripke-style semantics. Next, we provide set-theoretic completeness results for them.

Algebraic Kripke-style semantics for substructural fuzzy logics (준구조 퍼지 논리를 위한 대수적 크립키형 의미론)

  • Yang, Eunsuk
    • Korean Journal of Logic
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    • v.19 no.2
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    • pp.295-322
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    • 2016
  • This paper deals with Kripke-style semantics, which will be called algebraic Kripke-style semantics, for fuzzy logics based on uninorms (so called uninorm-based logics). First, we recall algebraic semantics for uninorm-based logics. In the general framework of uninorm-based logics, we next introduce various types of general algebraic Kripke-style semantics, and connect them with algebraic semantics. Finally, we analogously consider particular algebraic Kripke-style semantics, and also connect them with algebraic semantics.

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Weakening- free non-associative fuzzy logics: mica- norm (based) logics

  • Yang, Eun-Suk
    • 한국논리학회:학술대회논문집
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    • 2009.05a
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    • pp.38-66
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    • 2009
  • Weakening-free non-associative fuzzy logics, which are based on mica-norms, are introduced as non-associative substructural logics extending $GL_{e\bot}$ (Non-associative Full Lambek calculus with exchange and constants T, F) introduced by Galatos and Ono (cf. see [10, 11]). First, the mica-norm logic MICAL, which is intended to cope with the tautologies of left-continuous conjunctive mica-norms and their residua, and several axiomatic extensions of it are introduced as weakening-free non-associative fuzzy logics. The algebraic structures corresponding to the systems are then defined, and algebraic completeness results for them are provided. Next, standard completeness (i,e. completeness with respect to algebras whose lattice reduct is the real unit interval [0, 1]) is established for these logics by using Jenei and Montagna-style approach for proving standard completeness in [7, 18].

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Algebraic Routley-Meyer-style semantics for the fuzzy logic MTL (퍼지 논리 MTL을 위한 대수적 루트리-마이어형 의미론)

  • Yang, Eunsuk
    • Korean Journal of Logic
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    • v.21 no.3
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    • pp.353-371
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    • 2018
  • This paper deals with Routley-Meyer-style semantics, which will be called algebraic Routley-Meyer-style semantics, for the fuzzy logic system MTL. First, we recall the monoidal t-norm logic MTL and its algebraic semantics. We next introduce algebraic Routley-Meyer-style semantics for it, and also connect this semantics with algebraic semantics.

Standard Completeness for the Weak Uninorm Mingle Logic WUML (WUML의 표준적 완전성)

  • Yang, Eun-Suk
    • Korean Journal of Logic
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    • v.14 no.1
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    • pp.55-76
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    • 2011
  • Fixed-point conjunctive left-continuous idempotent uninorms have been introduced (see e.g. [2, 3]). This paper studies a system for such uninorms. More exactly, one system obtainable from IUML (Involutive uninorm mingle logic) by dropping involution (INV), called here WUML (Weak Uninorm Mingle Logic), is first introduced. This is the system of fixed-point conjunctive left-continuous idempotent uninorms and their residua with weak negation. Algebraic structures corresponding to the system, i.e., WUML-algebras, are then defined, and algebraic completeness is provided for the system. Standard completeness is further established for WUML and IUML in an analogy to that of WNM (Weak nilpotent minimum logic) and NM (Nilpotent minimum logic) in [4].

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Algebraic Kripke-Style Semantics for Weakly Associative Fuzzy Logics (약한 결합 원리를 갖는 퍼지 논리를 위한 대수적 크립키형 의미론)

  • Yang, Eunsuk
    • Korean Journal of Logic
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    • v.21 no.2
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    • pp.155-174
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    • 2018
  • This paper deals with Kripke-style semantics, which will be called algebraic Kripke-style semantics, for weakly associative fuzzy logics. First, we recall algebraic semantics for weakly associative logics. W next introduce algebraic Kripke-style semantics, and also connect them with algebraic semantics.

A new proof of standard completeness for the uninorm logic UL (Uninorm 논리 UL을 위한 새로운 표준 완전성 증명)

  • Yang, Eun-Suk
    • Korean Journal of Logic
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    • v.13 no.1
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    • pp.1-20
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    • 2010
  • This paper investigates a new proof of standard completeness (i.e. completeness on the real unit interval [0, 1]) for the uninorm (based) logic UL introduced by Metcalfe and Montagna in [15]. More exactly, standard completeness is established for UL by using nuclear completions method introduced in [8, 9].

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On the Standard Completeness of an Axiomatic Extension of the Uninorm Logic

  • Yang, Eun-Suk
    • Korean Journal of Logic
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    • v.12 no.2
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    • pp.115-139
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    • 2009
  • This paper investigates an extension of the uninorm (based) logic UL, which is obtained by adding (t-weakening, $W_t$) (($\phi$ & $\psi$) ${\wedge}$ t) $\rightarrow$ $\phi$ to UL introduced by Metcalfe and Montagna in [8]. First, the t-weakening uninorm logic $UL_{Wt}$ (the UL with $W_t$) is introduced. The algebraic structures corresponding to $UL_{Wt}$ is then defined, and its algebraic completeness is established. Next standard completeness (i.e. completeness on the real unit interval [0, 1]) is established for this logic by using Jenei and Montagna-style approach for proving standard completeness in [3, 6].

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Weakening-free fuzzy logics with the connective Δ (II): a variant of Baaz projection

  • Yang, Eunsuk
    • Korean Journal of Logic
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    • v.16 no.1
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    • pp.1-15
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    • 2013
  • Yang [12] investigated weakening-free fuzzy logics expanded by the delta connective $\Delta$, which can be interpreted as Baaz's projection and its generalizations. In this paper, we keep investigating such logics with an alternative delta connective $\Delta$, which can be regarded as a variant of the Baaz projection. The main difference is that although our new $\Delta$ satisfies many properties of Baaz projection, it can nether be interpreted as Baaz's projection itself nor its generalizations. For this, we first introduce several weakening-free fuzzy logics with the alternative connective $\Delta$. The algebraic structures corresponding to the systems are then defined, and their algebraic completeness is proved.

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Mianorm-based Logics with right and left n-potency axioms (좌 우, n-멱등 공리를 갖는 미아놈 논리)

  • Yang, Eunsuk
    • Korean Journal of Logic
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    • v.23 no.1
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    • pp.1-23
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    • 2020
  • This paper deals with mianorm-based logics with right and left n-potency axioms and their fixpointed involutive extensions. For this, first, right and left n-potent logic systems based on mianorms, their corresponding algebraic structures, and their algebraic completeness results are discussed. Next, completeness with respect to algebras whose lattice reduct is [0, 1], known as standard completeness, is established for these systems via Yang's construction in the style of Jenei-Montagna. Finally, further standard completeness results are introduced for their fixpointed involutive extensions.