Fw: LRML and alternative logics

From: Wyner A.Z. <A.Z.Wyner@Swansea.ac.uk>
Sent: Thursday, April 30, 2020 10:47 PM
To: Harold Boley <harold.boley@gmail.com>
Subject: Re: LRML and alternative logics

Hi Harold,

Great to hear from you and thanks so much for all your links and comments. Very helpful. I feel I've popped down the rabbit hole, and it will take some time to parse this. But, I see it is already a well-developed discussion, which is extremely useful and reassuring.

I'll try to understand this, then also relay it into the LRML TC, as there has clearly not been sufficient discussion about LRML and semantics/logic, which was punted. I think if it is not addressed appropriately, it will come back to haunt us.

Thanks again.

Regards,

Adam

-------------

Dr. Adam Zachary Wyner

Associate Professor of Law and Computer Science

Director of the Centre for Innovation and Entrepreneurship in Law

School of Law (Price 103 - Singleton) and Department of Computer Science (Computational Foundry 111 - Bay)

Swansea University

Swansea, United Kingdom

Orcid: https://orcid.org/0000-0002-2958-3428

Blog: https://azwyner.info/

Twitter: @AdamWyner

LinkedIn: Adam Wyner

From: Harold Boley <harold.boley@gmail.com>
Sent: Thursday, April 30, 2020 9:05 PM
To: Wyner A.Z. <A.Z.Wyner@Swansea.ac.uk>
Subject: RE: LRML and alternative logics

Hi Adam,

Thanks, I am fine. Hoping that you and your family and friends, and your/our colleagues are fine as well.

Tim Berners-Lee endorsed the first of the two Coronavirus articles of Tomas Pueyo, both of which still appear relevant:

https://medium.com/@tomaspueyo/coronavirus-articles-endorsements-fdc68614f8e3

Initially, Tara, Adrian, and I worked on RuleML Semantic Styles/Profiles.

Since Tara might no longer work on this, if you could (initially) bring Adrian into your response that would be great.

Your points are very relevant to the official spec:

http://wiki.ruleml.org/index.php/Specification_of_RuleML_1.02

http://wiki.ruleml.org/index.php/Predefined_Semantic_Styles_of_RuleML_1.02

Also, to some steps towards updates:

http://wiki.ruleml.org/index.php/Specification_of_RuleML_1.03

http://wiki.ruleml.org/index.php/Predefined_Semantic_Styles_of_RuleML_1.03

--should be-->

http://wiki.ruleml.org/index.php/Predefined_Semantic_ Profiles_of_RuleML_1.03

(we changed "Semantic Style" to "Semantic Profile", but didn't rename all pages and references to them)

Of the three (unfinished)

… semantic profiles that provide fully-specified semantics for their syntactic scope, have also been predefined in RuleML 1.03:

Horn-PSOA Tarski (http://ruleml.org/1.03/profiles/HornPSOA-Tarski)
Horn Logic Herbrand (http://ruleml.org/1.03/profiles/Horn-Herbrand)
First-Order Logic Herbrand (http://ruleml.org/1.03/profiles/FOL-Herbrand)

the most elaborate is the one for Herbrand Semantics:

http://wiki.ruleml.org/index.php/Horn_Logic_Herbrand_Semantic_Profile_of_RuleML_1.03

It comes with a mapping table:

http://wiki.ruleml.org/index.php/Horn_Logic_Herbrand_Semantic_Profile_of_RuleML_1.03#Presentation-to-XML_Syntax_Mapping

RE: The first subproblem

As demonstrated with the three above Semantic Profiles, all must have a "Syntactic Scope".

However, many RuleML or LRML Syntactic 'Scopes'/Languages have no Semantic Profile (yet).

One Syntactic Language can have several Semantic Profiles (your alternative interpretations), e.g. Tarski vs. Herbrand.

RE: The second subproblem

As in your disjunction exemplification:

Interoperation is usually Syntactic: only Language translation.

Interoperation should become (more) Semantic: add Profile translation

(cf. "stable model" vs. "well-founded" in https://www.w3.org/2005/rules/wiki/RIF_FLD_Dialects).

RE: … a third problem ... The problem is not about isomorphically translating one language to another, but to address a genuine, fundamental difference in meaning. ...

Indeed, much harder than the translation of Languages (and less often (completely) possible)

is the translation of Logics in the sense of

Logic = (Language,Profile) pairs,

a simplified meta-terminology I used instead of

Semantic Profile = "" class="x_GramE">,Syntactic Scope,Body,…) tuples, in

The RuleML Knowledge-Interoperation Hub. LNCS 9718, pp. 19-33. Springer, 2016. Abstract: https://link.springer.com/chapter/10.1007/978-3-319-42019-6_2. Preprint: http://ruleml.org/papers/RuleMLKnowleropHub.pdf. Slides: http://ruleml.org/talks/RuleMLKnowleropHub-talk.pdf

Stay Safe and in Good Health!

Best Wishes,

Harold

From: Wyner A.Z. [mailto:a.z.wyner@swansea.ac.uk]
Sent: Thursday, April 30, 2020 1:54 PM
To: Harold Boley
Subject: LRML and alternative logics

Hi Harold,

I hope you've been well and that the virus keeps far from you, your family, and friends.

I've been thinking further about the matter of LRML and alternative logics, which we raised in the last LRML telecoms. There seems to be some issues here to clarify.

I'm writing to you to help me sharpen my understanding and to hear your views, which I hope will help me better see and express what I think is going on in the current discussion. I'm not a logician, but I think I can get the main points well enough to ask questions that might need to be addressed.

Livio made it clearer to me that while we might have, for example, a disjunction represented in RuleML or LRML, we could have alternative semantics or different logics for the representation. OK, that is a point I get, as I've read about alternative semantics for disjunction (I've read Simons and Aloni a long while ago) and the conditional (I've read Edgington a long while ago) when I was doing more work on formal syntax and semantics of natural language. As a baseline, we can take information from entries in the SEP (again, my reading on these matters was a while ago, so I'm rusty on the substance):

https://plato.stanford.edu/entries/disjunction/

https://plato.stanford.edu/entries/conditionals/

OK, so that is background.

Let me layout some problems. Suppose I have a RuleML/LRML representation of some disjunctive statement, say that which correlates with P v Q. Let's say we have two alternative interpretations (derived from the above literature), i and j, of the semantics/logic of disjunction, which I'll represent as [P v Q]-i and [P v Q]-j, respectively. Let's suppose that [P v Q]-i and [P v Q]-j require different sorts of information to draw inferences (different 'input') and/or different inferences follow (different 'output'). (Note that 'input' and 'output' are terms of convenience, as I'm not using them in the sense of I/O Logic, which I've heard about not worked out). If these points were not so, then we would not have different interpretations of the logical connectives, as all purported different interpretations would simply be notational variants. So, we are really considering that the logical connectives are intensional, they have different meanings relative to the interpretation.

The first subproblem is that while LRML supports a representation of alternative interpretations of legal rules, this does not, so far as I understand, support the representation of alternative interpretations of the LRML logical language per se; at least, I've never heard this point raised. Let's suppose that we can indicate that there are alternative interpretations of the LRML language about, e.g. disjunction, by something schematically as I have above.

The second subproblem is that this isn't really what I need. Rather, what I need is to know exactly how the reasoning is done with respect to each of the interpretations of the logic of the disjunctive _expression_. After all, if I write [P v Q]-i, then I am saying that I am representing not just disjunction, but more essentially whatever reasoning and inferences that follow with respect to the i interpretation of disjunction. It is important not just to indicate that there is a different interpretation, but to make that interpretation explicitly applicable to the logical connective. After all, when I pass my LRML representation of my laws to someone else, I'm offering a way of reasoning with my legal information; that is, I want to make my information reproducible, transmittable, credible for integration into someone else's legal reasoning. In other words, the inferences that I intend to hold do hold with no additional, unknown alternative 'side effects'. What I don't want is that my idea of the legal reasoning, including the logic of disjunction, is read by someone else in some other way, leading to side effects that I did not intend in my interpretation of the laws. An alternative view on this is suppose I don't indicate an interpretation of the disjunction, along the lines of what we currently have, [P v Q], but I have 'in mind' a particular interpretation, e.g. i. Then this representation (without any indication of interpretation) is passed to someone else, who takes [P v Q], but under the interpretation *they* have in mind for disjunction, e.g. j. We could, for instance, draw very different inferences in each instance with respect to the different interpretations of disjunction. I don't want that at all since that violates the underlying purpose of having a 'common' language, which not only facilitates communication of symbols, but of meanings and content.

So, suppose I do communicate using the indices, that is, I encode my knowledge as [P v Q]-i. That isn't really sufficient, since what I really need to do is to communicate the whole logic that i represents - I need to tell others what my interpretation of v means. So, the logic of i needs to be encoded in RuleML/LRML itself and transmitted or linked to the file with [P v Q]-i. That would allow me to communicate about my logical interpretation of the rules.

That isn't really sufficient, which takes us to a third problem. Suppose that someone gets my file, but wants a different interpretation for disjunction, swapping out i and putting in j, resulting in [P v Q]-j. This is a bit weird to me as it is a move from a meaning that I gave to the knowledge for whatever purposes I had for it into a meaning that someone else has of the knowledge for other purposes. But, how can we be sure that there is compatibility across what the two parties know and their purposes? After all, the difference in logics (the i logic v j logic) are intended to reflect some difference and, perhaps, some incompatibility. For instance, there may be different inputs and outputs to each logic; what holds for one does not for the other. The problem is not about isomorphically translating one language to another, but to address a genuine, fundamental difference in meaning. However, that is at odds with communication of a standard - when I see [P v Q], I'm supposed to understand what that means and how my machine is to process the information.

One possibility is that we represent both the LRML representation with index and associated logic, e.g. [P v Q]-i and [P v Q]-j, specifying the inputs and outputs for each logic. Then the developer would indicate the intended interpretation. Others would be able to make their own choice. This would make transparent differences. It would be a 'meta' version of what seems to be done with the interpretation indicators currently available in LRML. It would require the encoder of the representations to provide all the requisite alternative inputs and consideration of the alternative outputs. That would be a lot of effort. This would require a significant development of LRML to represent the alternative logical interpretations. As researchers add additional logical interpretations, the language would need to be extended.

In a sense, such 'interlingua' issues are what standards are designed and intended to avoid. Here, it arises again due to the lack of agreement about what the syntax really represents. So, I don't see what the solution would be.

That's my outline of what I see at this point. Likely there is much that I fail to understand about how RuleML/LRML would handle such matters. Likely others have already discussed and solved this. But, the discussion so far in the LRML TC has not yet helped me understand what was at stake, much less how to resolve them. Rather, the discussion has proceeded in a rather isolated manner - two camps with their own logics that can be tied to LRML without a higher level consideration of the implications that serve the overall endeavour.

I hope that doesn't waste your time! I would be grateful for your thoughts and how I might share them with the LRML TC.

Take care! Stay healthy! Talk later.

Best, Adam