• 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].

• Korean Journal of Logic
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• v.12 no.1
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• pp.89-110
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• 2009

This paper investigates generalizations of weakening-free uninorm logics not assuming associativity of intensional conjunction (so called fusion) &, as non-associative fuzzy-relevance logics. First, the strong t-associative monoidal uninorm logic StAMUL and its schematic extensions are introduced as non-associative propositional fuzzy-relevance logics. (Non-associativity here means that, differently from classical logic, & is no longer associative.) Then the algebraic structures corresponding to the systems are defined, and algebraic completeness results for them are provided. Next, predicate calculi corresponding to the propositional systems introduced here are considered.

• 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.

• Korean Journal of Logic
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• v.11 no.1
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• pp.131-156
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• 2008

This paper first investigates several uninorm logics (introduced by Metcalfe and Montagna in [8]) as fuzzy-relevance logics. We first show that the uninorm logic UL and its extensions IUL, UML, and IUML are fuzzy-relevant; fuzzy in Cintula's sense, i.e., the logic L is complete with respect to linearly ordered L-matrices; and relevant in the weak sense that ${\Phi}{\rightarrow}{\Psi}$ is a theorem only if either (i) $\Phi$ and $\Psi$ share a sentential variable or constant, or (ii) both $\sim\Phi$ and $\Psi$ are theorems. We next expand these systems to those with $\triangle$.

• 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.

• Korean Journal of Logic
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• v.22 no.3
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• pp.397-415
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• 2019

This paper deals with the pretabular property of some fuzzy logics. For this, we first introduce the involutive idempotent uninorm logics IdIUL and IUML and examine the relationship between IdIUL and the another well-known system $RM^T$. Next, we show that IUML is pretabular, whereas IdIUL is not.

• 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.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2420-2422
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• 2003

In this paper, two Fuzzy Logics for path planning of an autonomous mobile robot are proposed. If a target point is given, such problems regarding the velocity and object recognition are closely related with path to which the mobile robot navigates. Therefore, to ensure safety navigation of the mobile robot for two fuzzy logic parts, path planning considering the surrounding environment was performed in this paper. First, feature points for local and global path are determined by utilizing Cell Decomposition off-line computation. Second, the on-line robot using two Fuzzy Logics navigates around path when it tracks the feature points. We demonstrated optimized path planning only for local path using object recognition fuzzy logic corresponds to domestic situation. Furthermore, when navigating, the robot uses fuzzy logic for velocity and target angle. The proposed algorithms for path planning has been implemented and tested with pioneer-dxe mobile robot.

• Korean Journal of Logic
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• v.19 no.3
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• pp.437-461
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• 2016

This paper investigates weakening-free fuzzy logics with three weak forms of associativity (of multiplicative conjunction &). First, the wta-uninorm (based) logic $WA_tMUL$ and its two axiomatic extensions are introduced as weakening-free weakly associative fuzzy logics. The algebraic structures corresponding to the systems are then defined, and algebraic completeness results for them are provided. Next, standard completeness is established for $WA_tMUL$ and the two axiomatic extensions with an additional axiom using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.17 no.1
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• pp.181-196
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• 2014

This paper deals with Kripke-style semantics for fuzzy logics. More exactly, I introduce algebraic Kripke-style semantics for some weakening-free extensions of the uninorm based fuzzy logic UL. For this, first, I introduce several weakening-free extensions of UL, define their corresponding algebraic structures, and give algebraic completeness. Next, I introduce several algebraic Kripke-style semantics for those systems, and connect these semantics with algebraic semantics.