1983 - Mapping Between Semantic Representations Using Horn Clause

Even after an unambiguous semantic interpretation has been computed for a sentence in context, there are at least three reasons that a system may map the semantic representation R into another form S. 1. The terms of R, while reflecting the user view, may require deeper understanding, e.g. may require a version S where metaphors have been analyzed. 2. Transformations of R may be more appropriate for the underlying application system, e.g. S may be a more nearly optimal form. These transformations may not be linguisticly motivated. 3. Some transformations structural context. depend on nonDesign considerations may favor factoring the process into two stages, for reasons of understandability or for easier transportability of the components. This paper describes the use of Horn clauses for the three classes of transformations listed above. The transformations are part of a system that converts the English description of a software module into a formal specification, i.e. an abstract data type. 1 RESEARCH SPONSORED BY THE AIR FORCE OFFICE OF SCIENTIFIC RESEARCH, AIR FORCE SYSTEM COMMAND, USAF, UNDER GRANT NUMBER AFOSR-80-O 19OC. THE UNITED STATES GOVERNMENT IS AUTHORIZED TO REPRODUCE AND DISTRIBUTE REPRINTS FOR GOVERNMENTAL PUPOSES NOTWITHSTANDING ANY COPYRIGHT NOTATION HEREIN. TRODUCTDON Parsing, semantic interpretation, definite reference resolution, quantifier scope decisions, and determining the intent of a speaker/author are well-known problems of natural langauge understanding. Yet, even after a system has generated a semantic representation R where such decisions have been made, there may still be a need for further transformation and understanding of the input to generate a representation S for the underlying application system. There are at least three reasons for this. First, consider spatial metaphor. Understanding spatial metaphor seems to require computing some concrete interpretation S for the metaphor; however, understanding the metaphor concretely may be attempted after computing a semantic representation R that represents the spatial metaphor formally but without full understanding. Explaining the system’s interpretation of a user input (e.g. for clarification dialog, allowing the user to check the system’s undersanding, etc.) is likely io be more understandable if the terminology of the user is employed. By having an intermediate level of understanding such as R, and generating English output from it, one may not have to recreate the metaphor, for the terms in R use it as a primitive. Second, the needs of the underlying application system may dictate transformations that are neither essential to understanding the English text nor linguisticly motivated. In a data base environment, transformations of the semantic representation may yield a retrieval request that is computationally less demanding [ 1 11. To promote portability, EUFID Cl31 and TQA [61 are interfaces that have a separate component for transformations specific to the data base. In software specification, mapping of the semantic representation R may yield a form S which is more amenable for proving theorems about the specification or for rewriting it into some standard form. The following example, derived from a definitron of stacks on page 77 of Cl 01 illustrates both of the reasons above. A stack is an ordered list in which all insertions and deletions occur at one end called the top. 424 From: AAAI-83 Proceedings. Copyright ©1983, AAAI (www.aaai.org). All rights reserved. A theorem prover for abstract data types would normally assume that the end of the stack in question is referred to by a notation such as A[ 11 if A is the name of the stack, rather than understanding the spatial metaphor “one end”. Third, it may be convenrent to design the transformation process in two phases where the output of both phases is a semantic representation. In our system, we have chosen to map certain paraphrases into a common form via a two step process. The forms “ith element” and “element i” each generate the same term as a result of semantic interpretation. However, the semantic interpreter generates another term for “element at position i” due to the extra lexical items “at” and “position”. Obviously, all three expressions correspond to one concept. The mapping component recognizes that the two terms generated by the semantic interpreter are paraphrases and maps them into one form. Section 2 gives an overview of the system as a whole. Section 3 describes the use of Horn clauses for the mapping from R to S. Related research and our conclusions are presented in sections 4 and 5. 2. BRIEF SYSTEM OVERVIEW The overall system contains several components beside the mapping component that is the focus of this paper. The system takes as input short English texts such as the data structure descriptions in [lo]. The output is a formal ;Ispecification clauses . of the data structure defined in Horn First, the RUS parser [3], which includes a large general-purpose grammar of English, calls a semantic component to incrementally compute the semantic interpretation of the phrases being proposed. As soon as a phrase is proposed by the grammar, the semantic interpreter either generates a semantic interpretation for the phrase or vetoes the parse. The only modifications to adapt the parser to the application of abstract data types were to add mathematical notation, so that phrases such as “the list (A [ 11, A[2], . . . . A [Nl I” could be understood. Thus, a text s%ch as the following can be parsed by the modified grammar . 2 Horn clauses are a version of first order logic, where all wellformed formulas have the form C IF Al & A2 & . . . & An. Each of the AI IS an atomic formula; C IS an atomic formula; and n>=CJ. Therefore, all variables are free. 3 Thts IS a modlfled version of a definition given on pages 41-42 of ClOl. 1. We say that an ordered list is empty or it can be written as (A[ 11, A[2], . . . . A [N]) where the AC11 are atoms from some set S 2. There are a variety of performed on these lists. operations that are 3. These operations include the following 4. Find the length N of the list. 5. Retrieve the ith element, lc=l<=N 6. Store a new value at the ith position, l<=l<=N. 7. Insert a new element at position I, l<=l<=N+ 1 causing elements numbered I, I+ 1, . . . . N to become numbered I+ 1, l+2, . . . . N+ 1. 8. Delete :he element at position I, l<=l<=N causing elements numbered I+ 1, . . . . N to become numbered I, I+ 1, ., N1. The semantic component we developed employs case frames for disambiguation and generation of the semantic interpretation of a phrase. However, the semantic component does not make quantifier scope decisions. Quantifier scope decisions, reference resolution, and conversion from first-order logic to Horn clauses is performed after the semantic interpreter has completed its processing. The knowledge governing these three tasks is itself encoded in Horn clauses and was developed by Daniel Chester. The output from this component is the input to the mapping component, which is the focus of this paper. In the appendix, examples of the Horn clause input to the mapping component are given for some of the sentences of the text above. The semantic representation R of a single sentence is therefore a set of Horn clauses. In addition, the model of context built in understanding the text up to the current sentence is a set of Horn clauses and a list of entities which could be referenced in succeeding sentences. The mapping component performs the three tasks described in the previous section to generate a set S of Horn clauses. S is added to the model of context prior to processing the next input sentence. The choice of Horn clauses as the formal representatron of the abstract data type is based on the following motivations: 1. Once a text has been understood, the set of Horn clauses can be added to the knowledge base (which is also encoded as Horn clauses). This offers the potential of a system that grows in power.