LOGICAL FORMS IN THE CORE LANGUAGE ENGINE Hiyan Alshawi & Jan van Eijck SRI International Cambridge Research Centre 23 Millers Yard, Mill Lane, Cambridge CB2 11ZQ, U.K. Keywords: logical form, natural language, semantics ABSTRACT from linguistic analysis that applies composi- tional semantic interpretation rules indepen- This paper describes a 'Logical Form' target dently of the influence of context. language for representing the literal mean- Sentence ing of English sentences, and an interme- ~, syntax rules diate level of representation ('Quasi Logical Parse trees Form') which engenders a natural separation semantic rules between the compositional semantics and the QLF ezpressions processes of scoping and reference resolution. ~, context The approach has been implemented in the LF expressions SRI Core Language Engine which handles the English constructions discussed in the paper. The QLF expressions are derived on the ba- sis of syntactic structure, by means of se- mantic rules that correspond to the syntax INTRODUCTION rules that were used for analysing the sen- tence. Having QLFs as a well-defined level of The SRI Core Language Engine (CLE) is representation allows the problems of com- a domain independent system for translat- positional semantics to be tackled separately ing English sentences into formal represen- from the problems of scoping and reference tations of their literal meanings which are resolution. Our experience so far with the capable of supporting reasoning (Alshawi et CLE has shown that this separation can ef- al. 1988). The CLE has two main lev- fectively reduce the complexity of the system els of semantic representation: quasi logical as a whole. Also, the distinction enables us to forms (QLFs), which may in turn be scoped avoid multiplying out interpretation possibil- or unscoped, and fully resolved logical forms ities at an early stage. The representation (LFs). The level of quasi logical form is the languages we propose are powerful enough target language of the syntax-driven seman- to give weU-motiwted translations of a wide tic interpretation rules. Transforming QLF range of English sentences. In the current expressions into LF expressions requires (i) version of the CLE this is used to provide a fixing the scopes of all scope-bearing opera- systematic and coherent coverage of all the tors (quantifiers, tense operators, logical op- major phrase types of English. To demon- erators) and distinguishing distributive read- strate that the semantic representations are ings of noun phrases from collective ones, and also simple enough for practical natural lan- (ii) resolving referential expressions such as guage processing applications, the CLE has definite descriptions, pronouns, indexical ex- been used as an interface to a purchase order pressions, and underspecified relations. processing simulator and a database query The QLF level can be regarded as the nat- system, to be described elsewhere. ural level of sentence representation resulting In summary, the main contributions of the 25 work reported in this paper are (i) the intro- for an elegant compositional semantic duction of the QLF level to achieve a natural framework: separation between compositional semantics and the processes of scoping and reference resolution, and (ii) the integration of a range use of lambda abstraction for the of well-motivated semantic analyses for spe- translation of graded predicates in cific constructions in a single coherent frame- our treatment of comparatives and work. superlatives; We will first motivate our extensions to first order logic and our distinction between use of tense operators and inten- LF and QLF, then describe the LF language, sional operators for dealing with illustrating the logical form translations pro- the English tense and au~liary sys- duced by the CLE for a number of English tem in a compositional way. constructions, and finally present the addi- tional constructs of the QLF language and illustrate their use. • Extensions motivated by the desire to separate out the problems of scoping from those of semantic representation. EXTENDING FIRST ORDER LOGIC • Extensions motivated by the need to deal with context dependent construc- As the pioneer work by Montague (1973) sug- tions, such as anaphora, and the implicit gests, first order logic is not the most nat- relations involved in the interpretation of ural representation for the meanings of En- possessives and compound nominals. glish sentences. The development of Mon- tague grammar indicates, however, that there is quite a bit of latitude as to the scope of the The first two extensions in the list are part extensions that are needed. In developing of the LF language, to be described next, the the LF language for the CLE we have tried to other two have to do with QLF constructs. be conservative in our choice of extensions to first order logic. Earlier proposals with simi- These QLF constructs are removed by the processes of quantifier scoping and reference lar motivation are presented by Moore (1981) and Schubert & Pelletier (1982). resolution (see below). The ways in which first order logic-- The treatment of tense by means of tempo- ral operators that is adopted in the CLE will predicate logic in which the quantifiers 3 and not be discussed in this paper. Some advan- V range over the domain of individuals--is ex- tages of an operator treatment of the English tended in our treatment can be grouped and motivated as follows: tense system are discussed in (Moore, 1981). We are aware of the fact that some as- • Extensions motivated by lack of ex- pects of our LF representation give what are pressive power of ordinary first order arguably overly neutral analyses of English logic: for a general treatment of noun constructions. For example, our uses of event phrase constructions in English general- variables and of sentential tense operators say ized quantifiers are needed ('Most A are little about the internal structure of events or B' is not expressible in a first order lan- about an underlying temporal logic. Never- guage with just the two one-place pred- theless, our hope is that the proposed LF rep- icates A and B). resentations form a sound basis for the subse- quent process of deriving the fuller meaning • Extensions motivated by the desire representations. 26 RESOLVED Leave(e, john) ^ Sudden(e))). LOGICAL FORMS The use of event variables in turn permits us to give a uniform interpretation of prepo- NOTATIONAL CONVENTIONS sitional phrases, whether they modify verb phrases or nouns. For example, John de- Our notation is a straightforward extension signed a house in Cambridge has two read- of the standard notation for first order logic. ings, one in which in Cambridge is taken to The following logical form expression involv- modify the noun phrase a house, and one ing restricted quantification states that every where the prepositional phrase modifies the dog is nice: verb phrase, with the following translations quant(forall, x, Dog(x), Nice(x)). respectively: To get a straightforward treatment of the quant(exlsts, h, collective/distributive distinction (see below) House(h) A In_location(h, Cambridge), we assume that variables always range over past(quant (exists, e, Ev(e), sets, with 'normal' individuals corresponding Design( e, john, h ) ) ) ). to singletons. Properties like being a dog can quant(exlsts, h, House(h) A be true of singletons, e.g. the referent of Fido, past(quant(exists, e, Ev(e), as well as larger sets, e.g. the referent of the Design(e, john, h) ^ three dogs we saw yesterday. In_location(e, Cambridge)))). The LF language allows formation of com- plex predicates by means of lambda abstrac- In both cases the prepositional phrase is tion: ,~x,\d.Heavy.degree( z, d) is the predi- translated as a two-place relation stating that cate that expresses degree of heaviness. something is located in some place. Where the noun phrase is modified, the relation is between an ordinary object and a place; in the case where the prepositional phrase mod- EVENT AND STATE VARIABLES ifies the verb phrase the relation is between an event and a place. Adjectives in pred- Rather than treating modification of verb icative position give rise to state variables in phrases by means of higher order predicate their translations. For example, in the trans- modifiers, as in (Montague, 1973), we follow lation of John was happy in Paris, the prepo- Davidson's (1967) quantification over events sitional phrase modifies the state. States are to keep closer to first order logic. The event like events, but unlike events they cannot be corresponding to a verb phrase is introduced instantaneous. as an additional argument to the verb pred- icate. The full logical form for Every repre- sentative voted is as follows: GENERALIZED QUANTIFIERS quant(forall, x, Repr(x), past(quant(exists, e, Ev(e), Vote(e,x)))). A generalized quantifier is a relation Q be- tween two sets A and B, where Q is insensi- Informally, this says that for every represen- tive to anything but the cardinalities of the tative, at some past time, there existed an 'restriction set' A and the 'intersection set' event of that representative voting. A N B (Barwise & Cooper, 1981). A gen- The presence of an event variable allows eralized quantifier with restriction set A and us to treat optional verb phrase modifiers as intersection set ANB is fully characterized by predications of events, as in the translation a function AmAn.Q(m, n) of m and n, where of John left suddenly: m = IAI and n = IANB I. In theLFlan- guage of the CLE, these quantifier relations past(quant(exists, e, Ev(e), are expressed by means of predicates on two 27 numbers, where the first variable abstracted The reading of Two companies ordered five over denotes the cardinality of the restriction computers where the first noun phrase is in- set and the second one the cardinality of the terpreted collectively and the second one dis- intersection set.