Textual Inference by Combining Multiple Logic Programming Paradigms Chitta Baral Gregory Gelfond Michael Gelfond Richard B. Scherl Dept. of C.S. & Eng. Dept. of C.S. Dept. of C.S. C.S. Dept. Arizona State University Texas Tech University Texas Tech University Monmouth University Tempe, Az 85287 Lubbock, Tx 7409 Lubbock, Tx 7409 West Long Branch, N.J. [email protected] [email protected] [email protected] [email protected] Abstract text and the background knowledge base. Finally, an answer is returned to the user. The goal of our approach to textual inference is to an- Here we propose a knowledge representation language swer queries about events and dates reported in texts; queries that demand inferencing with the relevant back- and an inference engine suitable for such a query answer- ground knowledge. Our primary knowledge representa- ing system. As the core knowledge representation language, tion language is AnsProlog. The core inference engine we propose AnsProlog - a language of logic programs un- is a combination of AnsProlog and Constraint Logic der the answer set semantics (Gelfond & Lifschitz 1988; programming. AnsProlog is particularly useful for the 1991). This language is especially useful if answering the representation of defaults, causal relations, and other query requires sophisticated kinds of reasoning such as de- types of common-sense knowledge. Constraint Logic fault, causal, counterfactual reasoning, reasoning about nar- Programming is needed to solve constraints involving ratives, etc. the relationship between the sequence of actions and The list of attractive properties of AnsProlog include its the dates on which the actions may have occurred. The combination of the two creates a useful tool for answer- simplicity and expressive power, ability to reason with in- ing quries over texts and in particular queries that in- complete information, existence of a well developed mathe- volve relatively deep reasoning. matical theory and programming methodology (Baral 2003), and the availability of rather efficient reasoning systems such as SMODELS(Niemela & Simons 1997b) and others Introduction and Motivation as well(Niemela & Simons 1997a; Lierler & Maratea 2004). We envision a query answering system which is given a text AnsProlog allows its users to encode defaults, causal rela- of some sort. This text may be typed into the system by the tions, inheritance hierarchies, and other types of knowledge user or it may have been retrieved by a search engine looking not readily available in other KR languages. There is also a for sources of information relevant to a query. well developed methodology for representing dynamic do- mains (Baral & Gelfond 2000; Turner 1997). In addition, it After the text is processed by the system, the user may supports the construction of elaboration tolerant knowledge then ask particular queries pertaining to the information in bases, i.e., ability to accommodate new knowledge without the text. Often the text will describe a series of actions or doing large scale surgery. events and the queries that the user wishes to pose will con- cern the truth of various facts about the world after these The main drawback of the language is the inability of its events have taken place or while they are occurring. An- current inference engines to effectively deal with numbers swering those questions demands commonsense reasoning and numerical computations. This is because the current an- and the use of commonsense knowledge about the world. swer set solvers start their computation with grounding the Generally, this commonsense knowledge is not contained in program, i.e. replacing its variables by possible ground in- the actual text. stantiations. The grounding algorithms are smart and capa- The approach is to initially translate the natural language ble of eliminating many useless rules; answer sets can be text (which we assume is in English) and the user’s query effectively computed even if the resulting program consists (also in English) into an appropriate knowledge representa- of hundreds of thousands of rules. However, if several inte- tion language. A knowledge base, also in the same knowl- ger variables are used by the program rules, the size of the edge representation language, is available. The knowledge grounded program becomes unmanageable. base needs to contain both commonsense and perhaps some Here we are concentrating on reasoning about texts that expert knowledge about the relevant domains. Then the in- involve actions and time. We not only have to reason about ference engine answers the user’s query by reasoning with the sequence of steps (individual actions) and what facts are both the representation of the information contained in the true after each step, but we also need to reason about dates and times. Since the number of dates is relatively large, the Copyright c 2005, American Association for Artificial Intelli- use of several rules that contain date variables quickly be- gence (www.aaai.org). All rights reserved. comes prohibitively inefficient. The same problem that oc- curs in general with numerical computations occurs in par- is false, an expression not l says that there is no reason to ticular with reasoning about dates and times. believe in l. We propose an architecture that combines the use of The answer set semantics of a logic program Π assigns to Π AnsProlog with (CLP) Constraint Logic Programming(Jaf- a collection of answer sets – consistent sets of ground liter- far & Lassez 1987; Van Hentenryk 1989; Marriott & als corresponding to beliefs which can be built by a rational Stuckey 1998; Fr¨uhwirth & Abdennadher 2002). CLP al- reasoner on the basis of rules of Π. In the construction of lows the use of efficient solvers over large and possibly infi- these beliefs the reasoner is guided by the following infor- nite domains while still preserving the declarative properties mal principles: of logic programming. The CLP portion determines which action steps correspond to which dates. • He should satisfy the rules of Π, understood as constraints Our implementation makes use of this combination of of the form: If one believes in the body of a rule one must AnsProlog and CLP. We have used the SMODELS imple- belief in its head. mentation of AnsProlog and the CLP module contained in • He should adhere to the rationality principle which says 1 Sicstus Prolog. We have also built a background theory in that one shall not believe anything he is not forced to be- AnsProlog sufficient to reason about a travel domain. This lieve. paper describes the architecture of our reasoning system and the background travel domain. It does not cover the transla- The precise definition of answer sets is first given for pro- grams whose rules do not contain default negation. Let Π tion of natural language text and queries into the AnsProlog, X nor does it cover the translation of the AnsProlog output into be such a program and a consistent set of ground liter- als. Set X is closed under Π if, for every rule (*) of Π, natural language. These are the topics of our current and fu- l ∈ X 1 ≤ i ≤ m l ∈ X ture work. 0 whenever for every , i and for every m +1≤ j ≤ n, lj ∈ X. Examples Definition 1 (Answer set – part one) A state X of σ(Π) is an answer set for Π if X is minimal (in Here is a simple example (Scenario 1) to illustrate the prob- the sense of set-theoretic inclusion) among the sets closed lem with which we are concerned. under Π. John is in Paris. On March 15th he packs his laptop To extend this definition to arbitrary programs, take any pro- in the carry-on luggage and takes a plane to Baghdad. gram Π, and consistent set X of ground literals. The reduct, Was his laptop in Baghdad on March 16th? ΠX ,ofΠ relative to X is the set of rules Depending on the time of the day, that John leaves Paris, he l ← l ,...,l may arrive in Baghdad on either March 15th or March 16th. 0 1 m X But it is a reasonable default assumption that in the absence for all rules (*) in Π such that lm+1,...,ln ∈ X. Thus Π of additional information John and his laptop remained in is a program without default negation. Baghdad after arriving. So, the desired answer is yes. But consider a variation on the above, Scenario 2. Definition 2 (Answer set – part two) X is an answer set for Π if X is an answer set for ΠX . On March 15th John took the plane from Paris to Bagh- dad. On the way the plane stopped in Rome, where Given, the translation of a text and a background theory, John was arrested. Is John in Baghdad on March 16th? the initial task of inferencing in AnsProlog is to compute all of the answer sets or models of the text and background Here we want to say no, because the arrest action would theory. To determine whether a fact follows from our text generally prevent John from continuing on to Baghdad. The and background theory, it is necessary to have a definition location of the laptop is more complex, but a good answer is of entailment. no. Of course to obtain this answer (rather than unknown), it is necessary to represent the background rule (a defeasible Definition 3 (Entailment) A program Π entails a literal l (Π |= l)ifl belongs to all rule) that when someone is arrested on a plane, the person’s Π carry-on luggage is taken off. answer sets of . The Π’s answer to a query l is yes if Π |= l, no if Π |= l, and We now introduce, AnsProlog and show how these exam- unknown otherwise.