On the Semantics of Hybrid ASP Systems Based on Clingo
Round 1
Reviewer 1 Report
The paper provides a general framework to make precise the semantic characterization of clingo's theory-reasoning, and its existing hybridizations, clingcon, clingoDL, clingoLP. For this they introduce the concept of abstract and structured theories to which they extend the stable models semantics. They provide a characterization of AMT with compositional theories, and then show how the formalism captures clingo's extensions. The framework is general enough that possible future hybrid systems can also be represented with it.
Given the lack of semantic foundation of these hybrid systems, the work is quite timely and highly relevant to the special issue. The paper is very clearly written, with examples throughout that help with understanding. Only Introduction seems to be on the short side. One wonders whether the motivation for the work could be elaborated more there, for example showing with an example the difficulty of finding a generic semantics that is meaningful for the existing hybrid systems. Other than that, the paper is in a good form to be accepted.
Author Response
Thank you for your comments!
We added the following paragraph to the introduction to more clearly outline the difficulties of finding semantics for hybrid systems:
"As a matter of fact,
most formal accounts of existing hybrid systems are implementation-driven
and lack a clear elaboration of the underlying semantic principles.
We address this by separating the semantic foundations of hybrid languages from the corresponding systems' design decisions.
As a result,
we present a framework in which we can characterize such decisions semantically."
An example of these different implicit semantics that we make clear can be found on Page 3 in the Background section.
Reviewer 2 Report
Paper is written clearly and logically. The main focus is given on the concept of anstract and structured theories which allow to formally elaborate their integration with answer set programming. Authors present an extension of logic programs and stable semantic models for those programs. Moreover, some types of abstract theories are classified. Finally, authors provide a discussion of how several existing asp systems can serve as a basis for their theoretical approach.
The introduction gives a lot of useful information - motivation, state of art, and the goals. Sections 2-4 are theoretical introduction and background. Section 5 is a core of the paper and section 6 conculdes the paper. All sections are written very well, paper contains necessary definitions and properties given in propositions, where particular proofs are in apendices.
Reviewer has only some formal recommendations:
- please, refer that proofs to propositions are in appendix
- formally, a part Conclusion is missing
- bad typography? empty space in counting lines from 53 to 54
- l. 43, bad stylistics Mote how, ... - please, reformulate the whole sentence
- l. 46, also "falsum" can be used
- bad notation, l. 46: authors say 0 <= i <= n, and b_0 can also be falsum which is different from any atom: why b0? then authors say b_i in A u T, and at once b0 can be falsum and falsum notin A u T??? Why also this set notation? I think all on lines 46-47 is written badly
- different fonts for operators, see e.g. (13) and l. 357, <= has two fonts
- did authors think in 6.1 blackbox orientation about formalizing by coalgebras? (one of the standard formal description of black box platforms)
- when orienting to fuzzy logic, did authors think also about the works of József Dombi and his formalizations of fuzzy logic? that approach would be very nice to analyze (maybe in future)
- generally, did authors think about axiomatic approach for formal modeling, as well?
Language issues (selected), paper needs deep proof-read
- l. 1: decades, (comma) ...
- l. 25: Meanwhile, this idea ...
- l. 34: stable model semantics -> "of" semantics / semantic models?
- l. 36: that are called / which we call
- more times in paper, "We" note (there is only Note ...)
- between l. 53-54 "we" envisage, "we" note etc.
- what is "viz"?
- l. 70: suppose "that" s is ...
- l. 120: Now, we provide ...
Author Response
Thank you for your comments!
We address each comment point by point below.
- please, refer that proofs to propositions are in appendix - Done
- formally, a part Conclusion is missing
We added summary section,
- bad typography? empty space in counting lines from 53 to 54
We cannot see the reason for this on our side, this will hopefully be fixed for the camera-ready version.
- l. 43, bad stylistics Mote how, ... - please, reformulate the whole sentence - Done
- l. 46, also "falsum" can be used - Done
- bad notation, l. 46: authors say 0 <= i <= n, and b_0 can also be falsum which is different from any atom: why b0? then authors say b_i in A u T, and at once b0 can be falsum and falsum notin A u T??? Why also this set notation? I think all on lines 46-47 is written badly -
Rewritten to "where $b_i\in\mathcal{A}\cup \mathcal{T}$ for $1 \leq i \leq m$ and~$b_0\in \mathcal{A}\cup\mathcal{T} \cup \{ \bot \}$ with $\bot \not\in \mathcal{A}\cup \mathcal{T}$ denoting the falsum constant.".
- different fonts for operators, see e.g. (13) and l. 357, <= has two fonts - Done
- did authors think in 6.1 blackbox orientation about formalizing by coalgebras? (one of the standard formal description of black box platforms)
Thank you for pointing that out, we have to look into that for future work.
- when orienting to fuzzy logic, did authors think also about the works of József Dombi and his formalizations of fuzzy logic? that approach would be very nice to analyze (maybe in future)
Again, thank you for the hint. There are many variants of fuzzy logic that can be explored in the future.
- generally, did authors think about axiomatic approach for formal modeling, as well?
Since the axioms change for every abstract theory, we do not immediately see how this would be done.
Smaller language issues have been addressed.
