Kutipan

APPROACH. MEANNG AS LOGICAL FORM In this section, we examine how logical approaches to meaning shed light on the basic issues of the content of semantic representations and the nature of grammatically relevant semantic properties. the logical study of meaning has along history, and here we can hope only to survey some of the results and present the spirit of logical analysis( clear accounts of logical semantics as a whole are given by allowed et al. 1977; and McCawley 1981) consequently, we limit our expotition to the nature and requirements of formal semantics, to certain general problems that formal semantics poses for the description of grammatical meaning in imperical terms, and in the end , to a consideration of how formal and nonformal semantics may be fruitfully brought together. Logic, Meaning , and formal Semantics why should we want to consider the meaning of an expression it is logical form, or it is representation in the mechanisms and formulas of logical analysis? there are two reasons: (a) logic is tipically concerned with truth, inference, and the content of expressions; (b)nlogic has an explicit and rigorous mealogical analysis and content there are inherent connection between logic and meaning because logic is concerned with conditions under which statments be truly inferred form other statments, Hence logic and the analysis of meaning involved there in are truth conditional. As a result of this goal, as McCawley (1981:1) remarks"logic is of nessessity concerned with semantic analysis, because semantic analysis directly affects our attemps to discover grammatically relevant semantic properties because we determine the presence or absence of such properties by making true inferences. Consider Tom punched bob and tom made contact with bob. we know intuitevely that if Tom punch implies"contact" How do we know this? we first determine the content of each expression by differentiating their status as statments ( from conveying true or false information ) from their status as sentences ( form with grammatical stucture.) we then analyze the relationship between the two expressions by making a series of inferences about their content; if Tom punched Bob, then there must have been contant between the two ; hitting necessarily involves contant, and so it must also be true that if Tom punched Bob, then he also made contact with Bob. Our conclusion rest on our ability to make judgments about likeness and difference of meaning, two goals traditionally whithin the scope of logic, such judgments are moreover, the cornerstone of all logic systems, which is the discovery of all neccessarily true inferences, or entailnents Logic realies on semantic analysis of the content of expressions to determine neccesarily true inferences. in this sense, semantics is a branch of logic . As such it buys into the second goald of logical analysis; to represent statments is a precise and unabiguous language.ns of representing the content of expression. Formal semantics and semantis representation Through system of logical analysis have different requirements, depending on their purposes and their assumptions abut inference and semantic content, they all typically have two parts ; a formal syntax and formal semantics. Both contribute to the logical form of expression. the formal syntax of a logical system is a set of a symbols, and rules for their proper combination , in which to represent the content of expressions. in proportional logic-a system for representing and analyzing entire sentences- there is vocabulary to represent the sontent of the sentences themselves , the proposions ( the symbols p,q,r) and connectives to express the combination of propositions V(or)-& (and) . in predicate logic- system for representing and analyzing the constituents of sentences- there is a vocabulary to express predicates, arguments, quantifiers as well the connectives of propositional logic. The formal syntax is complemented by an interpretation or a formal semantics. this is a way to connect the syntax to referents, and in doing so, to assign truth values to

expressions in the formal syntax. the semantic interperatation that form the basic of most current theories of logical form is a model, which is inan abstract spesification of the properties of a world to which expressions can in principle refer (whence the notion of model theoritic semantics) models gennerally cosist of t three sets of things ( or four , if the third is devided in two:(a) individuals to which the logical vocabulary can refer: for example , entities ,events, kinds, and so forth;(b) truth values : true or false , and in some models (trivalent logics) neither true nor false ;(C) worlds and times in which truth values and individuals occur : for example , then now, possibly then , and so forth . so when we say that the exprssion Tom puched Bob has meaning , in formal terms, we are saying that is syntactic forms(e.g. it is predicate and arguments, punh {Tom,bob} can be asigned referents form the set of individuals even and two entities) and have truth value in a certain world at a certain time(e.g. true prior to the moment of speech) To say the meaning discovered by looking at logical form , then it is to say that we have to see how an expression bears a relation to a model . more particulary, the meaning of an expression determines how the individuals referred to by the forms can be assigned truth values in a world at time (i.e, their truthconditions) in relating meaning the formal notion of the truth in a model formal semantics provides us with an explicit account of the content of semantic representations, the content of the model itself . indeed , formal semantics, as a theory of models, is often thought of by its adherents as equifalent to semantic theory in general. this view of meaning as a interpretation via a model brings with it a number of advantages . First, the content of semantic repretentations is made exact and ambiguous. certainly on e of the problems with in intutive account of meaning , like that we have impolyed thus far , is the room it leaves for error and subjective judgment, what does it mean to say that an expression denotes punctuality ? for 'puncuality' to be part of a formal theory of meaning , the notion must be clearly spesified somewhere in the model. the explication of meaning in terms of the logical forms of an expression is a restrictive theory of meaning it builds meaning forms the botton up the relies on only what is known to be part of the model to begin with. second, this account of meaning is formal , in that is independent of the content of what it represent and thus can be generally and mechanistically applied . the model is matematical object. Formal semantics speels out what is necessarily the case for interuption of an expression and investigates the constraints on the model as an idealized'denotational space', we want our semantic theories just to give us the general structure of meanings, not the specific content" this assumes that wha actually do in assigning to expressions is to apropriate and naturalize the ideal formal mormal model. the overall advantage of the formal characteristic of meaning is that semantic representations, though restrictive, are also quite general. third, if meaning is formal, then we can use the rest of the apparatus of formal analysis to solve standard semantic problems. a traditional goal of semantics is to account for intutitions we have about semantic relations between and within expressions. semantic likeness, difference , and inclusion ,examples of these relations are given here. a. likeness of meaning ; identity, Equivalence , or repettion 1, synonimy; equivalence or identity of words; e.g. couch and sofa. 2,paraphrase; eqiuvalence or identity of sentence ; e.g Bill ate the pizza was eaten byBill. 3.Tautology : invariant truth of an expression because of redudancy or rpetitio; Bill' brother is a sibling (sibling is redundant given the content of brother). B. Difference of meaning: oppositencess, exclusion, or incompatibility.

1. Antonym: oppositeness of word; e.g., alive versus dead and hot versus cold. 2. Contradiction: invariant falsity of an expression because of exclussion: e. g., Bills brother is his sister (the meaning of brother and sister exclude each other). 3. Anomaly: oddness of an expression because of incompatibility; e, g., Bills lawnmower murdered the flowers (innanimate lawnmowers are incompatible with the action of murdering an animate subject). C. inclusion of meaning 1. Hyponymy: set membership of words; e.g., couch of furniture (a couch is inluded in the set of furniture). 2. Entailment: invarianty true implication of a sentence because the first contains the second;e.g., Bill ran entails bill did something (running includes the notion of action and so an expression with run necessarily implies an prby bill is necessarily true and vice versa . synonyms are words that can be subtituted.for each other an expression whithout affecting the truth value ; i bought a'couch has the same truth conditions as I bougt a sofa. Furthermore, we can refine this concern for truth conditions to determine more subtle types of likness, difference, inclution of meaning. Lexical semanticist (those who study word meaning) typically identify two mayor kinds of antonymy- ungradable and gradable antonyms- determined by their truth conditions. ungradable antonyms are words whose meanings mutually exclude each other, lexical contradictions,denotations whit no middle ground.A standard test for such antonyms is as follows: the truth of one requires the falsity of the other(x-Y and Y- X) and the falsity of onw requires the truth of the other ( -X-Y and -Y-X) By this test, alive and dead are ungradable antonyms: if something is alive, it is not dead', if something is dead , it is not alive: if something is not alive, it is dead ", if something is not dead it is alive ungradable antonyms are sometimes called coplementaries because the complite each other in excluding the middle ground. if we slighly lossen the formal test for ungradable antonyms, we get gradable antonyms(or contraries) those that have a middle ground. for gradables, only the first part of the formal test for ungradables holds; the truth of one requires the falcity of the others. Hot and cold meet this simpler test: if something is Hot, it is not cold ", if something cold, it is not Hot note, however that if something is not hot ,then it not neccessarily cold, but, perhaps, warm. Hence, hot and cold are antonyms whit a middle ground, determined by the truth of the imperences that can be made from expression containing them ( she cruse 1986 for fulled discussion ). this final example return us to our original reasonession with do something). Formal semantics: we can anumerate that influences tha hold across statement trouhgt analysis of the content of the expression those those statments take. Semantics relations are all kinds of infernce and are calculated on the basis of the semantics repretentations of the expressions involved : long expression entails another because the semantics reprecentation

of one is a necesary semantic consequence of the semantic

representation of another . Formal semantics determines the nature or reprecentations proper, so inferences are made with respect to a model for interpretation and can be defined in relation. thereto. Two probllem with Formal semnaties We have seen how a formal aproach to meaning elusidates the nature and content of semantic representation. in partikular, wehave seen how the idea of a model as and abstract "the notatinal space" clarifies basic quetion of meaning. In spite of this great advantage, there are certain problems inherentin formal sematics. to say that a system is formal is to say that it is categorical and contentless. It these two features tha ultimately force apart formal semantics and linguistic semantic.

Before we discuss these two features in relation to linguistic meaning, we should be aware of an important caveat. Formal does mean 'formalism.' A popular method of debuking logic and of showing the diva variety ergence of formal and non formal semantic is to point out that the notation of formal semantic is insentive distinctions made in ordinary language. For example, it is easy to sow that predicate logi, the notation for quantifiers excludes of quantifiers that are otherwise found in ordinary languange.predicate logic has two quantifiers: the universal quantifier (' every/all '), and the exitential quantifier (' at least one/some ').The is no way to refresent the quantifiers many, a couple, several, and so on, quantifiers found commonly in everyday speech. Ist is sometimes thought that predicate logic and ordinary languange are simply imcompatible becouse of this absence. This is wrong. We could certainly develop a form of predicate logic that has symbols for these additipnal quantifiers. All we have to do is assign them a notation: M for many, S for several, and so on. The trick is not the notation. The formalism is arbitrary, and any phenomenon can can be refresented. The inadequacy of the notation of formal systems is a trivial objection. The heart of the matter lies in what makes the system formal, not in whatmakes the formalism. Categoricalness A formal system is categorical: The logical objects and operatins that populate a formal system have descrete boundaries. There is no overlap, and one object categorically axcludes another. For example, ~, logical negation, categorically reverses the truth value of whatever it attachhes to. There is no sense in propositional logic of more or less negation, or a gradience of falsity. The same may be said for the quantifiers in predicate logic. The universal quantifier A, for example, stands categorically for the totality of a set; the existential quantifier E categorically defines ' some' or ' at least one.' There is no gradience of quantification in predicate logic, just as there is no gradience of truth value for the negative operator in proposition. al logic. But if we look at ordinary language, We find that it is full of gradient phenomena, more technically

known as fuzziness (see Lakoff 1972 for the classic study; see also

Lakoff 1987, 1988; Jackendo of 1983: chap.7) the insight behing fuzziness indicates that categories have vague boundaries and are internally organizid from central focal value, the frototype (Rosch 1973, 1975), to less focal instances and fringe values. a category may be said to have degree of inclusiviness rather than strict criteria that ultimately draw a conceptual line beetween phenomena admitted and chose excluded. The need for gradience is especially pertinent inthe case of semantic categories, for in example, an account of natural language negation. Negation in formal semantries is categorical, but natural language requires degrees of negation. Two reliable tests of the presence of negation in English are: (1) coocurrence with any asopposed to some and (2) the eddition of a positive tag question (see horn; Klima1964; J. payne 1985; see also chap. 9) The following negative sentence takes both: 6. The senator did not take any bribes, did she/he?

However, when we look at english in more detail, we see that a variety of phenomena trigger these same tests, trough not all aqually, and not all trough explicit negation: 7. a. The senator seldom took any bribes, did/didn't she/he? b. The senator rarely took any bribes, did/didn't she/he Neither seldom nor rarerly is overtly negative (there is no not, as in [6], but they trigger any and so must have a negative in their semantic representation, sometime like 'not freqeuntly.' Unfortunately for the negative analysis, they also trigger both kinds of tag questnos. so, even though seldom and rarerly ere negative in some sense, they are totally negativthis picture is further complicated by the following: 8a. Rather than take any bribes, the senator resigned. b. Before the senator took any bribes, he/she covered his/her tracks. c. did the senator take any bribes? These sentences allow any, but they are allclearly positive and so there is no obvious need for a negative in their semantic representations. it might be argued. however, that rather is an implicit negative, expressing something like 'so as not to.' Before might also be argued to be negative, 'unrealized action.' A similar explanation also accounts for the acceptability of any with questions. Imformation questions are desaigned to indicate 'uncertainly,' strictly speakin another form of negation. Example ( 6-8 ) illustrate the gradient status of negaton. There is focal negation, or denial, signalled by not, which allows both reliable tests of negation. There are also markers of attenuated negation, like seldom and rarely: these take one of the test clearly and arguably one of the others . there are finally, markers of uncertainly and unrealization, a kind of a weak negation : not denial, but negation on the level of expectation. these also trigger a negative test. it seem clear, then, that ordinary language admits negation by degree, in such a case , the categoricalness in language, in this case, the formal nature of logical analysis prevents accurate description, and linguistic semantics, because it must deal with all there forms of negation , has to be nonformal on this count,e at least