Choice Rules and the Belief-Based View of ASP, Part 5 ========= Date: 1 Feb 2010 From: Michael Gelfond To: Marc Denecker I looked at your message carefully but I am afraid that I can not really come up with a meaningful response at this point. Two things are clear to me though. 1. I have to do much better job explaining my intuition behind the ASP connectives and the notion of answer set. 2. I have to spend more time trying to understand your alternative. At this moment I am not even sure if you are proposing to give a different interpretation to programs written in ASP syntax or suggesting that it would be better to replace ASP by your language FO(FD), etc. I also do not understand how objective view can be made compatible with non-monotonicity. So I need to read your papers again. There seems to be a substantial audience to our discussion and perhaps other people will have something to say on the subject. Below are some small comments and questions: > Suppose we want to feed our agent with the information that: > > either Ann or Dave belong to minorities. > > In classical logic, > > Minority(Dave) <-> -Minority(Ann). > > In ASP there are several representations. One is: > > Minority(Dave) <- not Minority(Ann). > Minority(Ann) <- not Minority(Dave). > > which means, e.g., for the first rule: > > If I (the system) does not believe that Ann is a minority, then > I believe that Dave is a minority. > > Another method is by using disjunction: > > Minority(Dave) | Minority(Ann) <- > > which is to be understood as: > > I believe that Dave is a minority or I believe that > Ann is a minority. From my standpoint neither of these ASP representations is epistemologically accurate. As far as I understand "either" in your statement means an exclusive or. So I'd encode it as: Minority(Dave) | Minority(Ann) -Minority(Dave) | -Minority(Ann) I find this rather natural. (Note that since the program does not contain "not" and for every answer set of this program and every atom P either P or -P belongs to this answer set (i.e. if there is no non-monotonicity and the agent is not allowed to ignore any atoms) the epistemic interpretation of the program coincides, I believe, with what you call the objective one.) > Therefore, to me, the mismatch between the human expert knowledge and its ASP representation > is a disturbing scientific problem. > > I think that the consequences of this mismatch are currently not well > understood in the ASP. But one is that many people now and in the > future will simply refuse to use ASP, just for this reason. There are > other consequences as well. They are not easy to show, especially not > to pragmatists (no offense ;-) ) because indeed, ASP works! I wouldnt > claim that I understand this very well but with what I understand, I > guarantee that it is in the long term interest of the ASP community to > reconsider this issue. A discussion of this is beyond the scope of > this email -- it is too long already- but if you are interested, then > lets explore this. I certainly do not want people to stop or refuse using ASP but I am not sure what I, personally, could do about it. Unfortunately I cannot honestly agree with something I do not understand. > As I understood it, > your aim with ASP was to design a pragmatically useful sublogic of AEL > and DL. Given the computational complexity of these two, you have > given up on expressivity in favour of efficiency. No, that never was my goal. My hypothesis was that classical connectives and classical logic as a whole is not suitable for the representation of non-mathematical knowledge. (For me it is still a very interesting hypothesis and that is one reason why I am interested in your work. If sufficiently developed it can prove me wrong.) There were of course some pragmatic questions but they were related to the language design and not to efficiency. For instance, Reiter's logic has a classical component, but it does not allow to use a disjunction A v B to reason by cases with defaults. In our paper on Disjunctive default logic we expanded Reiter's formalism by adding the ASP disjunction, A | B, which allows such reasoning. This immediately causes a question: what disjunction should we use to state that Bob or Mary is a minority? I believe that Wirth argued that in a good language every important natural language construct (i.e. a loop) should be expressed by exactly one formal construct. Disjunctive Default Logic violates this rule. Of course, this is just a historical comment, and not closely related to our discussion. > As for the first assumption (that genuine self-referential statements > are absent in most applications of ASP), you disagree, at least in > complex applications such as the USA-Advisor (but perhaps not for > graph coloring or hamiltonian path - confer your TAG email of 30 Nov > 2010). I think I see your point. In the USA-Advisor, assumptions are > made: closed world assumptions on data, default values, the inertia > rule. In the tradition started by Reiter, McDermott and Doyle, you > think of these assumptions as reflexive autoepistemic statements of > the agent. So, you use reflexive autoepistemic statements to build > elaboration tolerant representations of these types of common sense > knowledge. I see the sense of this, but I disagree with the price to > be paid: namely that every objective fact encoded in ASP turns into a > complex and unnatural autoepistemic proposition. I believe that reasonable people can disagree on this. > I've claimed that there is a very large class of ASP programs of which > their answer sets can be naturally interpreted as Tarskian Herbrand > interpretations representing possible states of the world. Such > programs were called ASP-world programs. My idea is that for such > programs, an alternative objective interpretation should exist. > > What could be the nature of this alternative interpretation? > Certainly, it should involve nonmonotonic constructs which allow to > build elaboration tolerant representations of assumptions of the above > kind. In various places (e.g., our paper in your anniversary symposium) > we have claimed that the concept of rule-based definitions is a suitable > construct (I know, I'm predictable :-)). > > This view can be explained also in your terminology. There is an intuitive > match between (formal) LP-functions and (informal) parametrized > definitions. They both define some concepts in terms of other > parameter concepts. All meaningful examples of LP-functions that I > have seen in your papers were representations of definitions (if I am > wrong then I would be glad to know). My claim is that ASP-world > programs can be viewed as a set of FO axioms (the constraints) plus > the union of a set of LP-functions plus Open World Declarations for > all predicates that are defined in none of the LP-functions. > The basics of this interpretation was worked out in: (although there is > room for improvement) > > Mariën, Maarten; Gilis, David; Denecker, Marc. On the relation between > ID-Logic and answer set programming, Logics in Artificial Intelligence, > 9th European Conference, JELIA 2004, volume 3229, pages 108-120, 2004 I'll try to look at it more carefully. At the moment I do not see how this takes care of non-monotonicity. > I agree with all you say. Yet, I dont see how this contradicts with my > idea that the USA-advisor is an ASP-world program. I think its answer > sets can be interpreted as Tarskian Herbrand interpretations > representing possible evolutions of the shuttle system. I think that > all assumptions that are made in the USA-Advisor are expressed well > (and of course equally elaboration tolerant) when interpreting the ASP > program in the above described way -as the union of LP-functions each > representing a definition, with constraints and open domain > declarations. In line with this I think that the expert knowledge > encoded in > it is inherently about material stuff (valves, tubes, reservoirs, > pressures, etc..) and does not need to involve self-reference to > what the knowledge base agent knows. So if the answer sets of a program represent all the possible worlds what happens when the agent learns that the component he believed to be o.k. is not or that the fluent which was supposed to be true after execution of some action is really false. What happens with his possible words? (I may just need to look again at your papers. You probably explain it there.) > This view seems to be consistent with what your wrote about the > USA-Advisor, as I mentioned in my email of 19 Nov 2010: > > + In the conclusion of the paper [1], it is written that: > "It was interesting to notice that many fluents of the > RCS domain had natural recursive definitions, easily expressible > in A-Prolog." > > [1] Marcello Balduccini, Michael Gelfond, Monica Nogueira, and Richard > Watson. Planning with the USA-Advisor. In 3rd International NASA > Workshop on Planning and Scheduling for Space, Sep 2002. > > + In a post on TAG on 22 Oct 2010, you expressed that the USA-Advisor > "was viewed by us as a collection > of LP-functions -- or in current terminology collection of modules. > LP function had a collection of input and output predicates and was viewed > as a mapping from some domain -- set of collections of input literals -- > to the set of collections of output literals". > > Combining both remarks seems to support my claim. Would you not agree? All this is certainly true. More of such discussion can be found in Marcello Balduccini, Michael Gelfond, and Monica Nogueira. Answer Set Based Design of Knowledge Systems. Annals of Mathematics and Artificial Intelligence, 2006. But in this paper we use CR-Prolog --- ASP with abduction. In the later version of ASP adviser we use P-log which expands ASP and CR-Prolog with the subjective view of probability. Do you want to give both of these languages objective interpretation too? > I agree with your view on agents. I disagree with the way you feed > knowledge in them. I think that the ASP-methodology makes it > impossible to compare KR in ASP and FO. I think the incomparability of > the ASP and FO methodologies is a real scientific problem. What is FO here? Is it first order logic or your language FO(ID) -- first-order logic with fix-point definitions? I am also suspect that in all these discussions we use the word "methodology" in a slightly different way. For me this is a more or less systematic method of solving a particular type of problems. It does not necessarily include philosophical analyses of basic notions. One can do mathematics without going deeply in the meaning of such notions as SET, Proof, Truth, etc. There was a methodology of solving algebraic equations even before people found an intuitive interpretation of imaginary numbers. Part of such methodology is: If you want to represent "either A or B" write A or B -A or -B I do not think that the paper on ASP methodology I mentioned above talks much about the meaning of ASP connectives. (Of course good understanding of intuition behind the language, connectives, etc is always useful.) It maybe that your understanding of methodology is slightly different. Anyway, I'll think more about the issues and try to better understand what you mean by "objective methodology". Any help with that will be appreciated. ========= Date: 7 Feb 2010 From: Marc Denecker To: Michael Gelfond Michael Gelfond wrote: > I looked at your message carefully but I am afraid that I can not really come up > with a meaningful response at this point. Two things are clear to me though. > 1. I have to do much better job explaining my intuition behind the > ASP connectives and the notion of answer set.` > 2. I have to spend more time trying to understand your alternative. > At this moment I am not even sure if you are proposing to give > a different interpretation to programs written in ASP syntax or > suggesting that it would be better to replace ASP by your > language FO(FD), etc. I will answer that at the end of this email. > I also do not understand how objective view can be made compatible > with non-monotonicity. > So I need to read your papers again. With an "objective" theory or formula, I mean one that does not speak explicitly about somebodies beliefs. Reiters defaults are not objective. A ; M B / C reads as: if A is known/believed/is derivable, and -B is not known/believed/derivable (i.e., it is consistent to assume B) then C. On the other hand circumscription is a formal logic principle which is non-monotone and objective. It does not refer to somebodies knowledge. A non-monotonic objective but *informal* natural language principle is the rule-based notation for (usually inductive) definitions (as you once told me, such definition may be understood to contain a final implicit rule "nothing else is a P", a kind of CWA,) > There seems to be a substantial audience to our discussion and perhaps > other people will have something to say on the subject. > > Below are some small comments and questions: > >> Suppose we want to feed our agent with the information that: >> >> either Ann or Dave belong to minorities. >> >> In classical logic, >> >> Minority(Dave) <-> -Minority(Ann). >> >> In ASP there are several representations. One is: >> >> Minority(Dave) <- not Minority(Ann). >> Minority(Ann) <- not Minority(Dave). >> >> which means, e.g., for the first rule: >> >> If I (the system) does not believe that Ann is a minority, then >> I believe that Dave is a minority. >> >> Another method is by using disjunction: >> >> Minority(Dave) | Minority(Ann) <- >> >> which is to be understood as: >> >> I believe that Dave is a minority or I believe that >> Ann is a minority. >> > > From my standpoint neither of these ASP representations is > epistemologically accurate. > > As far as I understand "either" in your statement means an exclusive > or. So I'd encode > it as: > > Minority(Dave) | Minority(Ann) > -Minority(Dave) | -Minority(Ann) > > I find this rather natural. > (Note that since the program does not contain "not" and for every > answer set of this program and every > atom P either P or -P belongs to this answer set (i.e. if there is no > non-monotonicity > and the agent is not allowed to ignore any atoms) the epistemic > interpretation of the program > coincides, I believe, with what you call the objective one. ) > Yes, I meant disjunctive or. Or, as in classical logic: Minority(Dave) <=> -Minority(Ann) Lets do an analysis to see compare these programs and see whether both programs are ASP-belief programs or ASP-world programs. The knowledge to be represented is "Either Dave or Ann (and not both) is a minority". What are the possible worlds of this knowledge? If this sentence is all we know and we assume that Ann and Dave are the two distinct elements of the universe, we get one possible world in which Dave is a minority and Ann is not a minority, and another one conversely. What literals do we believe if this information is all we know? None. So, a correct ASP-belief program will have the empty answer set {}. Obviously neither my own original two programs nor your alternative program are ASP-belief programs. They are ASP-world programs if their answer sets (after filtering away the classical negation literals -Minority(..) ) represent the possible worlds of this knowledge. The three programs have two answer sets, which differ only in the -Minority literals. After filtering out these literals, we obtain exactly the right possible worlds: one in which Dave is a minority and Ann is not, and one conversely. Hence, they are correct ASP-world representations of the given information. With epistemological adequacy, I think you mean that the informal semantics (the declarative reading) of the program should match intuitively with the given piece of information. With how I understand how ASP connectives are officially interpreted I think your encoding is to be interpreted as follows (please correct me if I am wrong): I believe that Dave is a minority or I believe that Ann is a minority I believe that Dave is a not a minority or I believe that Ann is not a minority Here "I" refers to the agent. Moreover there is always the implicit rationality assumption which could be phrased as: I do not believe anything unless I am forced to by my rules. This rationality assumption is used in one of my programs { Minority(Dave) or Minority(Ann)} so that at most one is believed yielding the exclusive or. Does this sound as a natural representation of "Either Dave or Ann are minorities"? First I'm struck by the complexity. As I claimed before, the original statement was objective in the sense that it does not refer to anybodies belief; in your ASP encoding (as well as in my two original ones) the representation is full of references to belief states of the agent. This confirms my earlier point: that encoding any piece of (objective) information in ASP turns it into a (complex) self-referential introspective epistemic formula(s). Also, it is obvious that the statements are false if the indexical *I* in these sentences ("*I* believe Dave ...") was to be me or you. Indeed, with the information given, both of us do *not* believe that Dave is a minority, and do *not* believe that Ann is a minority. This contradicts the first rule. So, if the rule is true for some *I*, then it must be the underlying agent of the program. So, I do not see much difference between your encoding and my original ones. The three programs "work" in the sense that we can derive the possible worlds from the answer sets. In your program, there are some additional classical negation literals, which are ignored in the process of extracting the possible worlds. But in my opinion, none of these programs has an accurate informal reading. Did I miss something? >> Therefore, to me, the >> mismatch between the human expert knowledge and its ASP representation >> is a disturbing scientific problem. >> >> I think that the consequences of this mismatch are currently not well >> understood in the ASP. But one is that many people now and in the >> future will simply refuse to use ASP, just for this reason. There are >> other consequences as well. They are not easy to show, especially not >> to pragmatists (no offense ;-) ) because indeed, ASP works! I wouldnt >> claim that I understand this very well but with what I understand, I >> guarantee that it is in the long term interest of the ASP community to >> reconsider this issue. A discussion of this is beyond the scope of >> this email -- it is too long already- but if you are interested, then >> lets explore this. >> > > I certainly do not want people to stop or refuse using ASP but > I am not sure what I, personally, could do about it. > Unfortunately I cannot honestly agree with something I do not understand. > >> As I understood it, >> your aim with ASP was to design a pragmatically useful sublogic of AEL >> and DL. Given the computational complexity of these two, you have >> given up on expressivity in favour of efficiency. > > No, that never was my goal. > My hypothesis was that classical connectives and > classical logic as a whole is not suitable for the representation of > non-mathematical > knowledge. (For me it is still a very interesting hypothesis and that > is one reason > why I am interested in your work. If sufficiently developed it can > prove me wrong.) > > There were of course some pragmatic questions but they were related to > the language design and not to efficiency. > > For instance, Reiter's logic has a classical component, but it does not allow > to use a disjunction A v B to reason by cases with defaults. > In our paper on Disjunctive default logic we expanded Reiter's > formalism by adding the ASP disjunction, A | B, which allows such reasoning. > This immediately causes a question: what disjunction should we use to state > that Bob or Mary is a minority? > I believe that Wirth argued that in a good language every important natural language > construct (i.e. a loop) should be expressed by exactly one formal construct. > Disjunctive Default Logic violates this rule. > > Of course, this is just a historical comment, and not closely related > to our discussion. Ok. I see. Regarding the (wide-held) hypothesis that FO is not suitable for the representation of non-mathematical knowledge. I think you as many others in the NMR community were far too radical. FO's connectives are direct formalizations of common NL connectives. It even shows in the definition of the truth relation: I|= F & G if I |= F AND I|=G which is essentially a (recursive) translation table from the logical connectives and quantifiers to natural language connectives. We need these base connectives, also for common sense KR. There are problems with FO for common sense reasoning, but it is not in how \land, \lor, \neg, \forall and \foreach are interpreted in FO (and not often in how => and <=> are interpreted). One problem is in the lack of "implicatures" made in FO (implicatures being implicit assumptions that we tend to make when we receive information); e.g., UNA, DCA, closures. Another is (or was) the lack of methodologies for elaboration tolerant representations rules with exceptions. Another problem is the set of expressivity gaps in FO (e.g., to express a transitive closure). Still it seems to me that FO, because of its correct treatment of basic NL connectives, is the kernel KR language. >> As for the first assumption (that genuine self-referential statements >> are absent in most applications of ASP), you disagree, at least in >> complex applications such as the USA-Advisor (but perhaps not for >> graph coloring or hamiltonian path - confer your TAG email of 30 Nov >> 2010). I think I see your point. In the USA-Advisor, assumptions are >> made: closed world assumptions on data, default values, the inertia >> rule. In the tradition started by Reiter, McDermott and Doyle, you >> think of these assumptions as reflexive autoepistemic statements of >> the agent. So, you use reflexive autoepistemic statements to build >> elaboration tolerant representations of these types of common sense >> knowledge. I see the sense of this, but I disagree with the price to >> be paid: namely that every objective fact encoded in ASP turns into a >> complex and unnatural autoepistemic proposition. >> > > I believe that reasonable people can disagree on this. > >> I've claimed that there is a very large class of ASP programs of which >> their answer sets can be naturally interpreted as Tarskian Herbrand >> interpretations representing possible states of the world. Such >> programs were called ASP-world programs. My idea is that for such >> programs, an alternative objective interpretation should exist. >> >> What could be the nature of this alternative interpretation? >> Certainly, it should involve nonmonotonic constructs which allow to >> build elaboration tolerant representations of assumptions of the above >> kind. In various places (e.g., our paper in your anniversary symposium) >> we have >> claimed that the concept of rule-based definitions is a suitable >> construct (I know, I'm predictable :-)). >> >> This view can be explained also in your terminology. There is an >> intuitive >> match between (formal) LP-functions and (informal) parametrized >> definitions. They both define some concepts in terms of other >> parameter concepts. All meaningful examples of LP-functions that I >> have seen in your papers were representations of definitions (if I am >> wrong then I would be glad to know). My claim is that ASP-world >> programs can be viewed as a set of FO axioms (the constraints) plus >> the union of a set of LP-functions plus Open World Declarations for >> all predicates that are defined in none of the LP-functions. >> The basics of this interpretation was worked out in: (although there is >> room for improvement) >> >> Mariën, Maarten; Gilis, David; Denecker, Marc. On the relation between >> ID-Logic and answer set programming, Logics in Artificial Intelligence, >> 9th European Conference, JELIA 2004, volume 3229, pages 108-120, 2004 > > I'll try to look at it more carefully. At the moment I do not see how > this takes care of > non-monotonicity. FO(ID) (the current name of ID-logic) contains formal definitions represented as sets of rules. Informal and formal definitions represented in this style are nonmonotonic: adding a case to a definition has a nonmonotonic effect. E.g., define the symmetric closure S of relation G: { S(x,y) <- G(x,y). S(x,y) <- S(y,x). } Suppose that G does not contain (a,b) nor (b,a), then this definition entails ~S(a,b). Suppose H contains (a,b), and we extend the definition of S with 1 rule: { S(x,y) <- G(x,y). S(x,y) <- S(y,x). S(x,y) <- H(x,y). } S nows defines the symmetric closure of the union of G and H and it now entails S(a,b). That is a nonmonotonic effect. One way to explain the nonmonotonicity is the hidden rule "Nothing else is an S" which is overruled in the second definition. Since inductive definitions comprise a form of CWA, strategies to encode exceptions and defaults can be simulated with them. The great thing about this form of CWA is that we apparently have a very good, precise common shared understanding of it -- it wouldnt be used in mathematics otherwisee. >> I agree with all you say. Yet, I dont see how this contradicts with my >> idea that the USA-advisor is an ASP-world program. I think its answer >> sets can be interpreted as Tarskian Herbrand interpretations >> representing possible evolutions of the shuttle system. I think that >> all assumptions that are made in the USA-Advisor are expressed well >> (and of course equally elaboration tolerant) when interpreting the ASP >> program in the above described way -as the union of LP-functions each >> representing a definition, with constraints and open domain >> declarations. In line with this I think that the expert knowledge >> encoded in >> it is inherently about material stuff (valves, tubes, reservoirs, >> pressures, etc..) and does not need to involve self-reference to what the >> knowledge base agent knows. > > So if the answer sets of a program represent all the possible worlds > what happens when the agent learns that the component he believed to > be o.k. is not or that the fluent which was supposed to be true after > execution > of some action is really false. What happens with his possible words? > (I may just need to look again at your papers. You probably explain it > there.) I am not sure if I understand you. At first the agent makes the assumption that the component is ok. According to this assumption any world in which the fluent is false is impossible, and the agent may reason and act accordingly. When discovering the mistake, he replaces his assumption with the real observed value. In his new state of mind the agent views any world in which the fluent is true as impossible. So the intersection of the possible worlds before and after revision is empty. This of course does not mean that there cannot be substantial pair-wise overlap between worlds thought to be possible before and after. And so, it might well be that most formulas that were true in all worlds before the revision are still true in all worlds after the revision. The crucial point is I think that the agent who is aware of where he makes assumptions will want to represent such assumptions in a elaboration tolerant way, so that they can be easily retracted or modified. But there are good methods and/or methodologies for this in objective logics. Think of completion, circumscription and yes, ... , definitions :-) >> This view seems to be consistent with what your wrote about the >> USA-Advisor, as I mentioned in my email of 19 Nov 2010: >> >> + In the conclusion of the paper [1], it is written that: >> "It was interesting to notice that many fluents of the >> RCS domain had natural recursive definitions, easily expressible >> in A-Prolog." >> >> [1] Marcello Balduccini, Michael Gelfond, Monica Nogueira, and Richard >> Watson. Planning with the USA-Advisor. In 3rd International NASA >> Workshop on Planning and Scheduling for Space, Sep 2002. >> >> + In a post on TAG on 22 Oct 2010, you expressed that the USA-Advisor >> "was viewed by us as a collection >> of LP-functions -- or in current terminology collection of modules. >> LP function had a collection of input and output predicates and was >> viewed >> as a mapping from some domain -- set of collections of input literals -- >> to the set of collections of output literals". >> >> Combining both remarks seems to support my claim. Would you not agree? > > All this is certainly true. More of such discussion can be found in > > Marcello Balduccini, Michael Gelfond, and Monica Nogueira. > Answer Set Based Design of Knowledge Systems. > /Annals of Mathematics and Artificial Intelligence/, 2006. > > But in this paper we use CR-Prolog --- ASP with abduction. > In the later version of ASP adviser we use P-log which expands ASP and > CR-Prolog with the subjective view > of probability. Do you want to give both of these languages objective > interpretation too? I dont know enough about the applications of these systems to answer this question right now. I have no doubt about the usefulness of these languages , just as that I have no doubts about the usefulness of ASP. My point here is that I believe that natural epistemic self-reference (i.e., references to what the agent knows or does not know in propositions that constitute the knowledge of an agent) in KR applications occurs but is rare and since it is so complex it is better not artificially introduced. We need languages in which we can write our knowledge in a semantically adequate way: i.e., the official informal semantics of our formal propositions match with the given information that they intend to encode. In the case of ASP, some thinking is required to redesign the language -keeping what is good- so that its informal semantics matches better with the information that people currently encode in ASP. I do not know enough about CR-prolog and P-log to say whether this might be necessary also for them. >> I agree with your view on agents. I disagree with the way you feed >> knowledge in them. I think that the ASP-methodology makes it >> impossible to compare KR in ASP and FO. I think the incomparability of >> the ASP and FO methodologies is a real scientific problem. > > What is FO here? Is it first order logic or your language FO(ID) -- > first-order logic with fix-point definitions? No, I meant FO, but the incomparability problem extends to all its extensions equipped with a Tarskian possible world semantics. > I am also suspect that in all these discussions we use the word > "methodology" in a slightly different way. > For me this is a more or less systematic method of solving a > particular type of problems. I made a mistake. I agree with your definition of "methodology" but misused the word in my statement. What I meant to say is: the primitive semantical concept of ASP is that of an answer set, which officially is to be interpreted as the set of all believed literals in some state of belief of some agent. This is a very different concept than the basic semantical notion of FO: that of a Tarskian structure representing a potential state of affairs. This in its own right makes it very difficult -nearly impossible- to compare ASP and FO formulas on the informal level, and hence to compare their methodologies. And if in addition, answer sets are used in practice in an unintended way as representations of possible worlds (which I have argued to be the case for most ASP programs, the ASP-world programs) then it becomes nearly impossible to peek through the mist. That is a real scientific problem in my opinion. > It does not necessarily include philosophical analyses of basic > notions. One can do mathematics without > going deeply in the meaning of such notions as SET, Proof, Truth, etc. > There was a methodology of solving algebraic equations even before > people found an intuitive interpretation > of imaginary numbers. > Part of such methodology is: > > If you want to represent "either A or B" write > > A or B > -A or -B > > I do not think that the paper on ASP methodology I mentioned above > talks much about the meaning of ASP connectives. > (Of course good understanding of intuition behind the language, > connectives, etc is always useful.) > It maybe that your understanding of methodology is slightly different. I agree with your view on methodology. I agree that the ASP methodology works. The real problem is that the ASP's theory of the informal semantics does not work: the nature of a piece of information and its representation is too different. I would not call this a "philosophical" problem (in the sense of "unwordly" that is sometimes associated with this term). E.g., some people refuse to use ASP because of its two "weird" negations that they cannot make sense of; this is a very practical problem that has to do with ASP's informal semantics problems. E.g., consider how this discussion started with: with a discussion on choice rules. It is completely obvious that in the current ASP methodology they are very useful. But what do they "mean"? They do not fit well in the official view of ASP as an autoepistemic language. This is caused by the mismatch between official views on informal semantics and the ASP methodology. So, what ASP needs in my opinion is: to find an alternative explanation of what an answer set means and what its connectives mean. I dont think this can be done without modifying the language somewhat, but I am absolutely sure that such a view and modified language can be developed and that the current methodologies (which do work!) can still be applied with only small superficial modifications. In fact, I am so sure because I consider FO(ID) to be such a language. > Anyway, I'll think more about the issues and try to better understand > what you mean > by "objective methodology". > Any help with that will be appreciated. > Very best, > M Thank you for your response. Let me finally say something about the question that you posed in the beginning. Do I want to replace ASP by FO(ID) or not? I would say: yes, replace ASP by FO(ID) and you will see that the current methodologies of ASP can be used with very small modifications. If you prefer the longer road, adapt ASP to make it objective and introduce support for constraints and for LP-functions to make it more suitable for KR; I predict one will end up in close proximity of FO(ID).