AILog User Manual Version 2.3 - UBC Department of Computer
Contents
1. X 2b 2b ch2 foo pl A Tall Person A term is either a variable a constant of of the form f t1 t where f a function symbol is a sequence of alphanumeric characters possibly including _ starting with a lower case letter and the t are terms An atom is either of the form p or p t t where p a predicate symbol is a sequence of al phanumeric characters including _ starting with a lower case letter and the t are terms Given this definition for atoms the rest of the syntax is the same as the propositional case Some predicate and function symbols can be written using infix notation For example X is 4 3 Y means the same as s X 4 3 Y where is is a predicate symbol and and x are function symbols The operator precedence follows Prolog s conventions AlLog User Manual Version 2 3 4 The symbol lt is defined to be infix but there are no clauses defining it This is designed to be used for meta programming where lt can be used as a meta level predicate symbol defining the object level implication See Artificial Intelligence Poole and Mackworth 2010 Chapter 13 4 Ask and Tell The general interaction with AILog is to tell it clauses and to ask it queries which are bodies It replies with answers which are instances of the query that are consequences of its knowledge base The user can then either explore how the system derived2. lt d X amp e X ailog askable e X ailog tell d a ailog tell d b ailog tell d c ailog ask a X Is e a true yes no unknown why help yes Answer a a Assuming c a more ok how help more Is e b true yes no unknown why help no Is e c true yes no unknown why help yes Answer a c Assuming c c more ok how help more No more answers ailog An explanation has to be consistent with the knowledge base To say that some body is not true you can use ailog tell false lt body AILog User Manual Version 2 3 16 Here false is a special atom that is false in all models Thus this clause provides a constraint specifying that the body is false From the set of constraints you need to create a set of nogoods to ensure that all explanations are consistent To do this you can issue the command ailog create_nogoods The nogoods correspond to the sets of assumables that imply false To list all of the nogoods you can issue the command ailog nogoods To debug the nogoods you can ask to prove false or ask whynot false 10 Negation as failure Negation as finite failure is implemented Use G to mean the negation of G G can be any body but must be ground i e contain no variables when G is called this may be fixed in future implementations The interaction of negation as failure and the depth bound is handled correctly There is a problem with negation and wh
3. Logical Approach Oxford University Press New York Poole D 2008 The independent choice logic and beyond In L De Raedt P Frasconi K Kersting and S Muggleton Eds Probabilistic Inductive Logic Programming Theory and Application LNCS 4911 Springer Verlag hnttp cs ubc ca poole papers ICL Beyond pdf Poole D L and Mackworth A K 2010 Artificial Intelligence foundations of computational agents Cambridge University Press New York NY http artint info
4. an answer or why the system didn t find another answer To add a clause to the knowledge base you issue the command ailog tell clause Example 1 You could tell the system some genealogy knowledge ailog tell parent X Y lt mother X Y ailog tell parent X Y lt father X Y ailog tell grandfather X Y lt father X Z amp parent Z Y ailog tell grandmother X Y lt mother X Z amp parent Z Y ailog tell father randy sally ailog tell father randy joe ailog tell mother sally mary ailog tell father joe sue You can ask a query to determine if some body is a consequence of the knowledge base ailog ask query where query is a body The system will respond with either an instance of the query that is a consequence of the knowledge base or No query doesn t follow from the knowledge base if there are no answers When the system have given an answer you can reply with ok to indicate that you don t want any more answers more to ask for more answers how to investigate how that answer was produced see Section 6 1 help to get a menu of available answers this option is available at all points where the system is asking for a response If you reply with more the system either finds another answer or reports there are no more answers Example 2 Given the knowledge base after Example I you can ask queries of the knowledge base ailog ask grandfather randy mary Answe
5. and for abduction probabilistic reasoning integrated with negation as failure Although it has similarities with Prolog it should not be seen as programming in logic but as repre senting in logic The tools are designed for the case where you are trying to model a domain in logic and can ask the system questions about what follows It can explain its reasoning in terms of the domain AILog is a purely declarative representation and reasoning system It is intended as a pedagogical tool to present a simple logic that can be used for AI problems It is meant for programming in the small where AlLog User Manual Version 2 3 2 you can axiomatize a domain ask questions and debug the knowledge base without knowing how answers are produced There may be sophisticated problem solving techniques used in finding answers We have many examples of probabilistic reasoning in AILog 2 as well as of the examples from the new book available The examples from cilog should also work 1 Getting and Starting AILog To start AILog just load the file ailog2 pl into Prolog Currently we have e ailog2 pl is currently at version 2 3 This runs on SWI Prolog version 5 3 or later e CILog version 1 is an older version that does not include probabilities but has versions that run in older versions of SWI Prolog and in Sicstus Prolog Try that if you have problems with this version e ailog21 pljis AILog version 2 1 which finds all expla
6. AILog User Manual Version 2 3 David Poole Department of Computer Science University of British Columbia Vancouver B C Canada V6T 1Z4 il poole cs ubc ca http www cs ubc ca poole September 27 2013 URL Abstract This manual describes AILog formerly CILog a simple representation and reasoning system based on the books Artificial Intelligence foundations of computational agents Poole and Mackworth 2010 and Computational Intelligence A Logical Approach Poole Mackworth and Goebel 1998 and the 2008 Independent Choice Logic for the probabilistic reasoning AILog provides e a definite clause representation and reasoning system e a simple tell ask user interface where the user can tell the system facts and ask questions of the system explanation facilities to explain how a goal was proved why an answer couldn t be found why a question was asked why an error producing goal was called and why the depth bound was reached knowledge level debugging tools that let the user debug incorrect answers missing answers why the system asks a question system errors and possible infinite loops depth bounded search that can be used to investigate potential infinite loops and used to build an iterative deepening search procedure sound negation as failure that interacts appropriately with the depth bound ask the user facilities assumables for finding conflicts e g in consistency based diagnosis
7. al Version 2 3 14 What is the value of age al value unknown why help 10 Answer young al amp young sally Runtime since last report 0 0 secs ok more how help how yes lt 1 young al 2 young sally How Number up retry ok prompt help 1 young al lt 1 age al 10 2 10 lt 13 How Number up retry ok prompt help 1 You told me age al 10 is true 8 Built in predicates There are a few built in predicates These cannot be redefined The following arithmetic predicates are predefined X lt Y where X and Y must be ground arithmetic expressions when called is true if the value of X is less than the value of Y X gt Y where X and Y must be ground arithmetic expressions when called is true if the value of X is greater than the value of Y X lt Y where X and Y must be ground arithmetic expressions when called is true if the value of X is less than or equal to the value of Y X gt Y where X and Y must be ground arithmetic expressions when called is true if the value of X is greater than or equal to the value of Y X Y where X and Y must be ground arithmetic expressions when called is true if the value of X is different to the value of Y V is E where E must be a ground arithmetic expression when called This is true if expression E evaluates to V number N where N is ground is true if N is a number Arithmetic expressions can either be numbers or of
8. ber up retry ok help how 2 h is a fact ie b Zee A How Number up retry ok help up d is used in the rule c lt Te it Ek DS a 3s O Number why help ok why c is used in the rule a lt 1 b tas 2 G Sree Number why help ok ok Depth bound reached Current subgoal e fail succeed proceed why ok help fail No more answers ailog 7 Ask the user The ask the user facility exists for yes no questions as well as for functional properties The subgoals have to be ground before being asked of the user This may be fixed in future implementations To to make an atom askable you can issue the command ailog askable atom Whenever a ground instance of the atom is attempted to be proved the user is asked if it is true The system may ask Is g true AlLog User Manual Version 2 3 13 The user can reply with one of yes if g is known to be true The system will not ask this instance again no if g is known to be false The system will not ask this instance again unknown if g is unknown In this case any applicable clauses for g can be used fail to fail the subgoal but not record an answer This is only used to test you axiomatization why to see why the system was asking this question This then enters the why interaction described in Section prompt to return to the ailog prompt help to get a menu of available answers Note the assumption that AILog makes about the interaction b
9. criptions of possible worlds where the possible worlds are described in terms of the prob abilistic atoms that are true in them and the descriptions are mutually exclusive This can be used form computing the probability of the query by summing over all of the worlds where it is true The worlds are computed from the explanations by making sure that they are mutually exclusive This can either be done after a prediction or observation or by issuing the command ailog worlds Which returns the worlds in which all of the observations are true Note that the ask command ignores all previous observations A future version may allow you to ask in the context of previous explanations You can undo observations using ailog unobserve which undoes the last observation or using ailog unobserve all which undoes all observations The command ailog probs AILog User Manual Version 2 3 18 lists all probabilistic assertions Note that probabilities integrates cleanly with negation as failure and naively with the depth bounded search It fails if the probability cannot be computed due to the depth bound A more sophisticated ver sion may give bounds on the probability Probabilistic hypotheses and non probabilistic hypotheses using assumable are not integrated and should not be used together Example 9 This may seem like not a very powerful probabilistic inference system however arbitrary Bayesian belief nets can be represented F
10. ct or a built in predicate see Section 8 or produces the instance of the top level rule that was used to prove the goal When you ask how atom h was proved it produces the instance of the rule in the knowledge base with has the head that succeeded h lt 1 aq 2 a2 k ak which indicates that the rule h lt a amp az amp amp ag was used to prove h You can then give one of how i where i is an integer 1 lt i lt k This means that you want to see how a was proved up to go back to see the rule with A in the body If A is the initial query it goes back to the answer interaction retry to ask for a different proof tree ok to exit the how traversal and go back to the answer prompt help for a list of the available commands If a was not proved via a rule for example if it was a fact or a built in predicate the reason that a was proved is printed and then the rule with a in the body is printed again Example 4 Given the knowledge base after Example I you can ask how a particular instance of the query was proved as in ailog ask grandfather G C Answer grandfather randy mary ok more how help how grandfather randy mary lt 1 father randy sally 2 parent sally mary How number up retry ok help how 2 parent sally mary lt 1 mother sally mary How number up retry ok help how 1 mother sally mary is a fact parent sally mary lt mother sally mary How number up ret
11. etween asking the user about g and using clauses for g It assumes that if the user knows whether g is true the user s answer should be used Any rules for g are used only if the user doesn t know whether g is true or not Example 7 The following gives the example of thejelectrical example with askables see 1998 page 214 ailog load ailog_code ch07 elect_askable pl Ailog theory ailog_code ch0O7 elect_askable pl loaded ailog ask lit L Is up s2 true yes no unknown why help yes Is up sl true yes no unknown why help no Is down s2 true yes no unknown why help no Is up s3 true yes no unknown why help yes Answer lit 12 ok more how help ok If f is functional i e if there can only be one value for f you can use the special syntax f V to mean that f has value V Then when you issue the command ailog askable f V Then a goal of the form f X will ask the user for the value of f once and remember the value For example ailog askable age P V ailog tell young P lt age P A amp A lt 13 ailog ask young sally amp young bruce What is the value of age sally value unknown why help 3 What is the value of age bruce value unknown why help 87 No young sally amp young bruce doesn t follow from the knowledge base Runtime since last report 0 0 secs ailog ask young al amp young sally AILog User Manu
12. first try to prove the leftmost conjunct If it fails we use the above whynot mechanism to determine why it failed If it succeeds the user is asked Should this answer lead to a successful proof The user can reply yes this instance should have made the body succeed Thus you need to debug the rest of the conjunction no this instance should lead to a failure of the body Thus you need to try another proof for this atom debug this instance is false debug it This enters the how interaction ok to return to the top level help to get a menu of available answers Example 5 Suppose we had the knowledge base from Example i Suppose that the user knew that Joe had a child called Jane and wanted to know why the system didn t think that Randy was Jane s grandfather We could imagine the following dialogue ailog whynot grandfather randy jane grandfather randy jane lt father randy A amp parent A jane Trace this rule yes no up help yes The proof for father randy sally succeeded Should this answer lead to a successful proof yes no debug help no The proof for father randy joe succeeded Should this answer lead to a successful proof yes no debug help yes parent joe jane lt mother joe jane Trace this rule yes no up help no parent joe jane lt father joe jane Trace this rule yes no up help yes There is no applicable rule for fat
13. have succeeded for this query no to ask for another rule You give this answer if this rule should have failed for this query up to return to a previous choice point the rule in which the atom appears or else the top level if the atom was the initial query ok to return to the top level help to get a menu of available answers If you answer no to each rule this means that all of the rules in the knowledge base should have failed and so the appropriate rule for the query that should have succeeded is missing To determine why a rule failed we determine why the body failed If the body is atomic we use the above whynot mechanism to determine why the rule failed If the body of the rule is a conjunction a amp B there are four cases e a fails in which case we should use recursively use the whynot mechanism to determine why it failed AlLog User Manual Version 2 3 9 e an instance of succeeds but should not have succeeded In this case we can use the how mechanism to debug this proof This case arises because B may have rightfully failed on the instance of that succeeded e an instance of succeeds but this instance should have lead to failure of the conjunction In this case we should look for another proof for a e an instance of succeeds that should lead to the success of the conjunction in which case we need to determine why failed on this instance Thus when there is a conjunctive body we
14. her joe jane parent joe jane lt father joe jane Trace this rule yes no up help up grandfather randy jane lt father randy joe amp parent joe jane Trace this rule yes no up help up ailog lt AlLog User Manual Version 2 3 10 6 3 Depth Bound The search strategy used by AILog is a depth bounded depth first search The depth bound is set using the command ailog bound n where n is a positive integer n is a bound on the depth of any proof tree The default value is 30 When a goal is asked and no more answers can be found if the depth bound was not reached the system reports there are no more answers If the depth bound was reached there still may be some answers although it is more likely that there is a bug in the knowledge base where some recursions do not terminate AILog allows the user to interactively explore the places where the depth bound was reached When no more answers can be found and the search was cut off due to hitting the depth bound the user is informed of this as is given the option of one of i where i is an integer bigger than the current depth bound This lets the user explore larger search trees Repeatedly increasing the depth bound lets the user simulate an iterative deepening search where to let the user explore the place where the depth bound was reached ok to go back to the answer prompt help for a list of the available comma
15. ical predicates One useful command to check your knowledge base is the command ailog check This lists the rules in the knowledge base with atoms in the body which don t unify with the head of any clause in the knowledge base or any askable or assumable This is a simple check that the rule can never be used in a proof This is useful as this is usually an indication that there is a problem with the knowledge base This static check replaces the dynamic undefined predicate exception of Prolog but is more useful in that it can be done before asking any queries it finds clauses that contain atoms that must immediately fail even if there are other clauses with the same predicate symbol The warning can be ignored if that is what you intended for example if you intend to add appropriate clauses later 6 Explanation and Debugging The main power of AILog is in the explanation and debugging facilities These fall into three classes e determining how an answer was proved e determining why a potential answer wasn t produced e determining why the search is in a particular state Each of these is described in the following sections AlLog User Manual Version 2 3 7 6 1 How Questions When the system has derived an answer you can ask how that answer was produced This provides a mechanism for interactively traversing a proof tree At each stage the system either says why the answer was produced immediately e g if it was a fa
16. nations and so does not work for large examples e the whole distribution at Attp artint info code ailog zip 2 Help and Exiting The basic system prompt is ailog 6609 This means that AILog is waiting for input from the user All user inputs end with a period and a return enter At any stage you can ask for help by issuing a help command ailog help This gives a brief description of the available commands To quit AILog you can issue the command ailog quit AILog is written in Prolog To exit AILog to the underlying Prolog you can use the command ailog prolog To restart AILog you should use the command start at the prolog prompt Note that this does not clear the knowledge base To turn on reporting the run time of queries you can do There weren t any when this manual was written but one of the design goals is that we should be able to use for example constraint satisfaction techniques to solve goals without needing to change the user level view of the system It may just run faster or not as the case may be AILog User Manual Version 2 3 3 ailog stats runtime On some systems this is the elapsed time since the query was asked or the user asked for more answers which may be a very inaccurate of run time if there was user interaction To turn off reporting of run time you can do ailog stats none 3 Syntax Atoms start with lower case letters and can include letter
17. nds When the user given the where command the proof is retried and it halts at a point where the depth bound was reached and shows the user the current subgoal g The user can give one of the following commands fail to fail g and explore other places where the depth bound was reached succeed to say that g should succeed proceed to fail g and not explore any more subgoals where the depth bound was reached why to let the user explore why g was called see Section 6 4p ok to go back to the answer prompt help for a list of the available commands 6 4 Why Questions If you find yourself at a particular subgoal it is often useful to find out why that subgoal is being proved When you ask why an atom was being asked AILog produces the instance of the rule in the knowledge base with the atom in the body such that the head was trying to be proved This is of the form h lt 1 aq 2 a xx ji aj k ak AILog User Manual Version 2 3 11 This means that a is the atom that is being asked the atoms a aj have been proved and aj41 ap have still to be proved When this is presented you can ask one of how i where i is an integer 1 lt i lt j This means that you want to see how a was proved This enters the how dialog how j This means that you want to see how AILog is trying to prove a the atom you have previously asked why about This returns to the rule with a in the body why to see
18. or example a belief network with Boolean variable A as a parent of variable B can be represented as ailog tell b lt a amp bifa ailog tell b lt a amp bifna ailog prob a 0 6 ailog prob bifa 0 9 ailog prob bifna 0 3 You can ask the prior on a using ailog predict a Answer P a Obs 0 6 Runtime since last report 0 03 secs ok more explanations worlds help ok And conditioning on b ailog observe b Answer P b Obs 0 34 Runtime since last report 0 secs ok more explanations worlds help ok ailog predict a Answer P a Obs 0 176471 Runtime since last report 0 secs ok more explanations worlds help ok ailog Thus P a b 0 176471 Note that Ailog does not find all explanations but only those within a threshold This threshold can be queried and varied with the prob_threshold command 11 1 Experimental Probabilistic Features The features in this section are only for specialized applications and may be changed in future applications Do not use these unless you know what you are doing Sometimes we may observe arbitrary choices that we don t want to model the probability of For exam ple that the rooms in an apartment are r17 753 and rs We may have a probability that there are three but the names may be arbitrary Once these have been observed then queries about what are the rooms should return these AlLog User Manual Version 2 3 19 As anothe
19. r grandfather randy mary ok more how help ok It has thus told you that grand father randy mary is a consequence of the knowledge base AILog User Manual Version 2 3 5 ailog ask grandfather joe mary No grandfather joe mary doesn t follow from the knowledge base which means grand father joe mary is not a consequence of the knowledge base You can ask queries with free variables ailog ask grandfather G C Answer grandfather randy mary ok more how help more Answer grandfather randy sue ok more how help more No more answers This means there are two instances of the query grand father G C that are consequences of the knowledge base 5 Loading and Listing Knowledge Bases You can also tell the system a set of clauses from a file The command ailog load filename where filename is the name enclosed in single quotes of a file that contains a sequence of clauses each clause ending with a period adds the clauses to the knowledge base as though they had been told to the system Note that the file does not contain tell commands it just contains the clauses Within files and at any prompt comments can be included between a and the end of a line or between x and x Loading a file adds the clauses to the database It does not replace definitions To clear the knowledge base you can issue the command ailog clear To remove all clauses wi
20. r example we may want to count rooms Which is the first room and which is the second room is arbitrary but we have to record which ones we have already counted so we don t count them again We don t want to search over the choices of which is first and which is second ailog arbitrary f V means that the values V assigned to f are arbitrary but f can only have one such value Note that f V can be used as any other atom The command arbitraries list all of the arbitrary declarations 12 Copyright AILog is free This means that everyone is free to use it and free to redistribute it on certain conditions AILog is not in the public domain it is copyright as follows Copyright 1997 2013 David Poole AILog is free software you can redistribute it and or modify it under the terms of the GNU General as published by the Free Software Foundation either version 2 of the license or at your option any later version This program is distributed in the hope that it may be useful but without any warranty without even the implied warranty of merchantability or fitness for a particular purpose See the GNU General Public License for more particulars A copy of the GNU General Public License can also be obtained from the Free Software Foundation Inc 675 Mass Ave Cambridge MA 02139 USA This documentation was written using Hyperlatex References Poole D Mackworth A and Goebel R 1998 Computational Intelligence A
21. ry ok help up grandfather randy mary lt father randy sally AILog User Manual Version 2 3 8 2 parent sally mary How number up retry ok help how 1 father randy sally is a fact grandfather randy mary lt 1 father randy sally 2 parent sally mary How number up retry ok help up Answer grandfather randy mary ok more how help more Answer grandfather randy sue ok more how help ok ailog 6 2 Whynot Questions Just as how questions let you explore the proof tree for a particular derivation whynot questions let you explore the search tree This facility is mainly used for determining why there was no proof for a particular query As such the documentation is written assuming that you are trying to determine why a query failed when you thought that it should have succeeded If a query fails when it should have succeeded either there was a rule defining the query whose body fails when it should have succeeded or else there is a missing rule for that query You can ask a query to determine why some query failed using ailog whynot query where query is a body If the query is an atom you can examine each rule whose head unifies with the query For each such rule the system asks whether you want to trace this rule You can reply with yes to determine why this rule failed You should give this answer when this rule should
22. s numbers and underscore _ A body is either an atom of the form amp f where and B are bodies or of the form a where is a body A clause is either an atom or is a rule of the form h lt b where h is an atom the head of the clause and b is a body 3 1 Individuals and Relations AILog can be used for propositional reasoning but can also be used for relational reasoning The syntax of variables and predicates is based on Prolog s syntax in its convention for variables but uses a different syntax for operators because Prolog s are so confusing and to emphasize AILog is not Prolog A variable is a sequence of alphanumeric characters possibly including that starts with an upper case letter or _ For example X Letter Any_cat A_big_dog are all variables The variable _ in an anonymous variable which means that all occurrences are assumed to be different variables If a variable occurs only once in a clause it should probably be written as _ A constant is either er e 9 e a sequence of alphanumeric characters possibly including as david comp_intell ailog anda45_23 starting with a lower case letter such e an integer or float such as 123 5 1 0 3 14159 4 5E7 0 12e 8 and 12 0e 9 There must be a decimal point in floats written with an exponent and at least one digit before and after a decimal point e any sequence of characters delimited by single quotes suchas
23. tance of these atoms must be ground We also allow statements where the probability is free for example in AILog User Manual Version 2 3 17 ailog prob heads_happens E P P This is useful when we want to learn parameters from observations Note that when this is called P must be bound There are two main interfaces to the probabilistic reasoning ailog observe obs where obs is a body This declares that obs has been observed This returns the probability of obs conditioned on all previous observations Observations accumulate so that subsequent queries and observations are with respect to all previous observations You can ask the posterior probability of a query this is the conditional probability given all of the current observations using ailog predict query where query is a body This gives the posterior probability of guery conditioned on all previous observa tions Given any prediction or observations you can inspect the explanations of the query An explanation corresponds to a proof of the query based on a set of the probabilistic atoms For each of these explanations you can examine the proof tree and ask how that explanation was computed This can either be done after a proof or as a stand alone command ailog explanations which returns the explanations of all of the observations You can also ask for the worlds in which the query and all of the previous explanations are true This gives a set of des
24. th head atom from the knowledge base you issue the command ailog clear atom To list the contents of the knowledge base you can issue the command ailog listing This gives a listing of the whole knowledge base that is suitable for copying to a file and loading in a subsequent AILog session To get a listing of all clauses in the knowledge base whose head unifies with atom you can issue the command ailog listing atom Note that in listings and any time atoms with free variables are written the variables are renamed The system does not remember the names you gave the variables It just calls them A B C etc AlLog User Manual Version 2 3 6 Example 3 Suppose the file genealogy cil contains the rules from Example 1 The following shows how the file can be loaded and listed ailog load genealogy cil AILog theory genealogy cil loaded ailog listing parent A B lt mother A B parent A B lt father A B grandfather A B lt father A C amp parent grandmother A B lt mother A C amp paren father randy sally father randy joe father joe sue ailog mother sally mary To load a file that uses Prolog syntax you can issue the command ailog prload filename This assumes the clauses in the file use the Prolog implication and use a comma for conjunction This does not allow the use of Prolog extra log
25. the form E E2 E1 E2 Ei E2 E1 E2 sin E log E etc Example 8 The following shows a simple use of is and gt It shows how we can use variables in the expressions as long as they are bound before to the left they are used ailog ask X is 3 4 5 amp X 2 gt 11x3 Answer 23 is 3 4 5 amp 23 2 gt 11 3 AILog User Manual Version 2 3 15 The restriction that the arithmetic expressions must be ground when called is severe and probably won t be fixed in future implementations There is one non arithmetic comparison e X Y true if X and Y denote different objects under the unique names assumption X and Y must be bound enough to determine whether they can be unified Delaying is not implemented This may be fixed in future versions 9 Assumables Assumables can be used for proof by contradiction or for abduction Integrity constraints rules that imply false are handled specially in abduction The interaction between assumables and negation as failure is not as general as it could be for the goal g any proof or partial proof of g should not depend on any assumables To to make an atom assumable you can issue the command ailog assumable atom When the atom is encountered it is assumed to be true The assumptions used to make a proof go though are collected and presented to the user when the answer is returned ailog tell a X lt b X amp c X ailog assumable c X ailog tell b X
26. the rule with h in the body prompt to return to the AILog prompt help for a list of the available commands Note that you can t ask how i for i gt j as there is no proof tree for the atoms aj ax Also AILog does not guarantee that the rule given will have the atoms in the body in the same order as in the knowledge base AILog is free to change the order of atoms in a body as long as this doesn t introduce an error Example 6 The following shows a trace of a looping program that reaches the depth bound We first increase the depth bound and then explore where the depth bound was reached ailog tell a lt b amp c amp d ailog tell b lt e ailog tell e ailog tell c lt f amp d amp g ailog tell f lt b amp h ailog tell h ailog tell d lt a ailog ask a Query failed due to depth bound 30 New depth bound where ok help 50 Query failed due to depth bound 50 New depth bound where ok help where Depth bound reached Current subgoal e fail succeed proceed why ok help why e is used in the rule b lt xx lie Number why help ok why b is used in the rule a lt kk Fip Zee 3 da Number why help ok why a is used in the rule d lt AILog User Manual Version 2 3 12 xx 1 a Number why help ok why d is used in the rule c lt Tiari xx 2 d Zing Number why help ok how 1 f lt Lip aah How Num
27. y questions sometimes the rule written out omits some negation symbols This only occurs when non atomic formulae are negated The interaction of negation as failure with assumables isn t as general as possible it is only sensible if you make sure that any proof for a negated atom does not include assumables Negation as failure does work with probabilities 11 Probabilities AILog contains support for first order probabilistic reasoning You can have probabilities associated with atoms that have no associated rules defining them There atoms are grouped into disjoint sets that correspond to random variables You can define these probabilistic assumptions using either ailog prob atom probability where atom is a atomic symbol and probability is a number between 0 and 1 atom can contain variables in which case every ground instance is a proposition with the corresponding probability All instances of the same atom and all atoms defined in different prob declarations are assumed to be probabilistically independent The alternative syntax is to write ailog prob a pl dz po Ak Pk Where the p are non negative numbers that sum to and the a are atoms that share the same variables In this case every ground instantiation of the a s forms a random variable the a s are mutually exclusive and covering The atoms defined in a prob statement cannot be used in the head of rules but can be used in the body When called the ins
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