Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics

Round 1

Reviewer 1 Report

The paper produces a fuzzy logics extension of algebraic Routley–Meyer-style (ARM for simplicity) semantics for basic substructural logics, as defined in [44] by the author. The main research question is posed in page 3 and its solution is fairly valuable. I believe that it lies in the field of interest of the special issue “Mathematical Fuzzy logic in the Emerging Fields of Engineering, Finance, and Computer Sciences” of Axioms.

The Introduction and presentation of results is quite authoritative, and the paper is written in good English by a reputed scholar in the field. Finally, the author poses two questions for future research at the end of the Concluding remarks (or section 4).

Author Response

To the reviewer #1,

I appreciate for your helpful comments and suggestions, I have improved my manuscript. I have given more detailed responses to your comments and suggestions. For this, please see the “=> parts” as my responses to the comments.

Comments and Suggestions for Authors

The paper produces a fuzzy logics extension of algebraic Routley–Meyer-style (ARM for simplicity) semantics for basic substructural logics, as defined in [44] by the author. The main research question is posed in page 3 and its solution is fairly valuable. I believe that it lies in the field of interest of the special issue “Mathematical Fuzzy logic in the Emerging Fields of Engineering, Finance, and Computer Sciences” of Axioms.

=> Thank you for your positive comment. I further add several reasons to consider ARM semantics fur substructural fuzzy logics (see the yellow part in p. 3).

The Introduction and presentation of results is quite authoritative, and the paper is written in good English by a reputed scholar in the field. Finally, the author poses two questions for future research at the end of the Concluding remarks (or section 4).

=> Again, thank you for your positive comment. I gave some more detailed explanation for future works together with one more future research (see the yellow parts in p. 18).

Please see the attachment for the emphasis of my responses.

Author Response File: Author Response.pdf

Reviewer 2 Report

A extension of the algebraic Routley–Meyer semantics to fuzzy logic is proposed.

The author should highlight more in the introduction the objectives of his research and the reasons that led him to explore the U-RM and F-RM semantics. 

Furthermore, in section 3 it is necessary to insert a meaningful example that shows how the two ARM semantics manage fuzzy systems. Paragraph 3.3 should become a new section in which the author discusses the advantages and limitations of U-RM and F-RM semantics; the paragraph is too short and the discussion of the advantages and limitations needs to be deeper. Also in the description of the limitations and advantages of the two ARM semntics it is useful for the author to include significant examples. For example, you need to enter an example that shows how the F-RM semantics can cover systems that the U-RM semantics cannot cover.

In section 4 it is not clear whether it is the author's intention in the future to analyze the connection between semantics for implicational tonoid fuzzy logics and those for substructural core fuzzy logics. What are, in terms of future prospects, the further research that the author intends to deepen? 

Author Response

To the reviewer #2,

I appreciate for your helpful comments and suggestions, I have improved my manuscript. I have given more detailed responses to your comments and suggestions. For this, please see the “=> parts” as my responses to the comments.

Comments and Suggestions for Authors

A extension of the algebraic Routley–Meyer semantics to fuzzy logic is proposed.

The author should highlight more in the introduction the objectives of his research and the reasons that led him to explore the U-RM and F-RM semantics.

=> Following your comment, I highlighted more the objectives and the reasons by giving some more statements for highlighting and some more reasons (see the yellow part in p. 3 together with the ones in pp. 1-2).

 

Furthermore, in section 3 it is necessary to insert a meaningful example that shows how the two ARM semantics manage fuzzy systems.

=> Following your comment, I gave two examples Examples 3 and 4 together with some statements associated with them (see the yellow part in p. 11 and the yellow part in p. 14).

 

Paragraph 3.3 should become a new section in which the author discusses the advantages and limitations of U-RM and F-RM semantics; the paragraph is too short and the discussion of the advantages and limitations needs to be deeper.

=> Following your comment, I deleted Section 3.3 and instead gave a new section Section 4. In particular, I introduced two subsections: one is advantages and limitations in general (Section 4.1) and the other is advantages and limitations in specific (Section 4.2) (see the yellow partd in pp. 15 - 17).

 

Also in the description of the limitations and advantages of the two ARM semntics it is useful for the author to include significant examples. For example, you need to enter an example that shows how the F-RM semantics can cover systems that the U-RM semantics cannot cover.

=> Following your comment, I gave two examples Examples 5 and 6 together with some statements related to them (see the yellow parts in pp. 16 - 17).

 

In section 4 it is not clear whether it is the author's intention in the future to analyze the connection between semantics for implicational tonoid fuzzy logics and those for substructural core fuzzy logics. What are, in terms of future prospects, the further research that the author intends to deepen?

=> Following your comment, I gave some more statements (see the two yellow parts in the third paragraph in p. 18).

 

Please see the attachment for the emphasis of my responses.

Author Response File: Author Response.pdf

Reviewer 3 Report

>The introduction should present additional details of the issues related to algebraic Routley-Meyer semantics. It should also cite similar papers.

>The advantages of the proposed concept should be highlighted.

>Please improve the description of the symbols.

>Could you provide some examples of real applications of the proposed techniques?

Author Response

To the reviewer #3,

 

I appreciate for your helpful comments and suggestions, I have improved my manuscript. I have given more detailed responses to your comments and suggestions. For this, please see the “=> parts” as my responses to the comments.

 

Comments and Suggestions for Authors

 

>The introduction should present additional details of the issues related to algebraic Routley-Meyer semantics. It should also cite similar papers.

=> Following your comment, I present additional details of the issues and cited similar papers (see the yellow part in p. 3).

 

>The advantages of the proposed concept should be highlighted.

=> Following your comment, in order to highlight the more detailed advantages (and limitations), I deleted Section 3.3 and instead gave a new section Section 4. In particular, I introduced two subsections: one is advantages and limitations in general (Section 4.1) and the other is advantages and limitations in specific (Section 4.2) (see the yellow partd in pp. 15 - 17).

 

>Please improve the description of the symbols.

=> Following your comment, I gave descriptions for the symbols in the second paragraph in Section 2, gave names for each axioms in Definition 1, and changed some notations, e.g. T to Γ for theories and RM to F for filters, to avoid confusions between formulas and sets of formulas, and between an abbreviation of Routley-Meyer and frame (see the yellow parts in Section 2 in pp. 4-6 in Section 2 and the yellow parts in Section 3 in pp. 7-14 ).

 

>Could you provide some examples of real applications of the proposed techniques?

=> Following your comment, I gave some related statements as one paragraph. But this is only a theoretical consideration but not a practical one. This is my current limit as a theorist (see the last paragraph in p. 18).

 

Please see the attachment for the emphasis of my responses.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Author improved the quality of this manuscript by incorporating all my suggestions, fully highlighting the objectives of his research and inserting significant examples that show the benefits and disadvantages of the two ARM semantics. I consider this paper publishable in the present form.