Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.1
Integrating Lexical Semantics and Formal Semantics.
Case Study I: The Dynamics of Adjective Meaning
0. Introduction ..............................................................................................................................................................1
1. Integrating formal semantics, lexical semantics, natural language metaphysics ......................................................1
1.1. Formal semantics in the broader setting of natural language use. ......................................................................1
1.2 Lexical semantics in the Moscow school............................................................................................................2
1.3 Meaning postulates. ............................................................................................................................................2
2. Introduction to adjective semantics .......................................................................................................................3
3. Adjective classification.............................................................................................................................................4
3.1. Meaning postulates for classes of adjectives ......................................................................................................4
3.2. Is tall intersective or subsective?. .......................................................................................................................6
4. Conclusions ...........................................................................................................................................................6
References .....................................................................................................................................................................6
Homework #2, Due March 6 .........................................................................................................................................8
0. Introduction
Initial working hypothesis: at least one central ingredient of the meaning of a sentence
must be a specification of the conditions under which it is true, and therefore one central
ingredient of word meanings must be their contribution to the truth-conditions of sentences.
One challenge for formal semanticists is to show cognitive scientists that in spite of the
nomenclature, and in spite of the anti-psychologism of some of the contributors to the
enterprise (Frege, Montague), linguists who are formal semanticists are very much engaged
in the investigation of human language competence. Greater attention to lexical semantics
and to the integration of lexical and formal semantics are crucial parts of this challenge.
One important challenge faced by compositional approaches such as formal semantics
is how to account for context-dependent meaning shifts without abandoning
compositionality. We argue here that in fact compositionality can be seen as one of the
driving forces in context-sensitive meaning shifts. Our case study will be the semantics of
different kinds of adjectives. The interplay of context-dependence and intensionality will be
illustrated in showing why skillful is intensional but large is not, even though we may
consider a large house not to be a large building. In a later lecture we will also take up the
puzzles of “privative” adjectives like fake and counterfeit and “redundant” adjectives like
real. The perspective we will take is how attention to the semantics of syntactic structure
(compositional semantics) sheds light on the word meaning, and how compositional
semantics, lexical semantics, and the context of the utterance all interact. One of the broader
implications of this perspective is that there should in principle be no conflict between the
goals of “formal” and “cognitive” approaches to semantics, although there are of course
differences in priorities and in favored forms of argumentation.
1. Integrating formal semantics, lexical semantics, natural language
metaphysics
1.1. Formal semantics in the broader setting of natural language use.
(1)
Model structures: arising from the way humans schematize situations they want to
describe.
When we view a natural language as a formal language, we simultaneously view the
world (or the set of possible worlds) as a model of it. This involves some abstraction and
NZ3Adjbetter.doc
1
March 1, 2006
Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.2
regimentation both of the language and of the world(s), as reflected in the type structure
imposed on the language and the ontology of the model structures in which it is interpreted.
Ideally, this abstraction should mirror a “real” abstraction which our “language
faculty” imposes on the real world, “natural language metaphysics” (Bach 1986) or naivnaja
kartina mira ‘naive picture of the world’ (Apresjan 1986).
(2)
We consider a sentence or a text as a theory describing the model of the situation
(model of this theory) (Borschev and Partee 1998)
(3)
This theory is formed from several sources:
ƒ text itself, its sentences are considered as formulas (formal semantics)
ƒ meaning postulates corresponding to words of text (lexical semantics)
ƒ contextual information (formal pragmatics in Montague’s sense)
The interaction of these constituents may be rather complicated.
1.2 Lexical semantics in the Moscow school.
• Lexical definitions in the Moscow school1 are modeled as mathematical definitions,
giving necessary and sufficient conditions. We believe that the “and sufficient” part is
probably too strong, and unrealistic.
• It is usually although not essentially assumed that there are some undefined notions,
semantic primitives (atoms of meaning). We are neutral but skeptical on this point.
• Meanings of other words are described by lexical definitions. Such a definition is a text
describing necessary and sufficient conditions, distinguishing presuppositions from
entailments.
• We represent the meaning of the word as a set of meaning postulates, the theory of this
word. This is our version of the Moscow school approach. We believe that meaning
postulates can capture linguistically important necessary conditions, without commitment
to providing sufficient conditions. Meaning postulates can be written in such a way as to
distinguish presuppositions from entailments, although we do not illustrate that here. We
illustrate some properties and uses of meaning postulates below.
1.3 Meaning postulates.
(i) Meaning postulates can specify semantic properties that distinguish various semantic
subclasses within a given semantic type, such as the following two classes of adjectives.
(a)
∀x∀P[skillful(P)(x) → P(x)] (a skillful surgeon is a surgeon; this
meaning postulate does not apply to adjectives like former and alleged.)
(b)
∀x∀P[former(P)(x) → ¬P(x)] (former is a “privative” adjective)
(ii) A meaning postulate with enough information packed into it may constitute a definition;
if the meaning postulate specifies necessary and sufficient conditions, it can be written with
an “iff” (↔) rather than just as a one-way implication.
∀x∀P[former(P)(x) ↔ [PAST(P(x)) & ¬P(x)]]
Whether such meaning postulates are possible for more than a small fraction of the lexicon of
a natural language is a matter of debate.
1
The Moscow school approach to lexical semantics is described in such works as (Apresjan et al. 1969,
Apresjan 1974, Apresjan 1992, Apresjan 1994, Apresjan 1995, Apresjan 2000, Mel'chuk 1974, Mel'chuk 1982,
Mel'chuk 1988, Mel'chuk and Zholkovsky 1984, Žolkovsky and Mel'chuk 1966). We emphasize the Moscow
school approach here because one of the long-term goals of our joint work with our Russian colleagues is a
synthesis of compositional and lexical semantics, particularly Western formal semantics and Moscow-school
lexical semantics.
NZ3Adjbetter.doc
2
March 1, 2006
Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.3
(iii) Meaning postulates can put constraints on the interrelations that must hold among the
meanings of certain words without necessarily treating one word as “more basic” than
another or decomposing both of them into some common “atoms”. Decompositional analyses
are not forbidden but are not required; that issue can be open to exploration and debate. The
meaning postulate below, for instance, is a way to say that the husband relation and the wife
relation are converses of each other without making one of them more basic than the other or
requiring decomposition into more elementary terms.
∀x∀y[husband(y)(x) ↔ wife(x)(y)]
2. Introduction to adjective semantics
Montague (1970b) presented a semantic treatment of adjectives which he credited to
unpublished work done independently by Hans Kamp and Terence Parsons; that work, and
similar independent work of Romaine Clark, was subsequently published (Clark 1970, Kamp
1975, Parsons 1970). The central claim in that work was that adjective meanings should be
analyzed as functions from properties to properties. Among adjective meanings, some might
satisfy further constraints such as intersectivity or subsectivity, but no such constraint can be
imposed on the class as a whole, the argument goes, because of the existence of adjectives
like false, ostensible, alleged.
The strategy of “generalizing to the worst case”, followed by Montague in order to have a
uniform assignment of semantic types to syntactic categories, called for giving all adjectives
the type of functions from properties to properties. More restricted subclasses of adjectives,
such as the subsective (skillful, good) and intersective (purple, carnivorous) adjectives, might
be indicated by the use of meaning postulates. In theories which allow type multiplicity and
type-shifting, the intersective adjectives might indeed be assigned the simpler type of oneplace predicates; this is now widely assumed.
Kamp and Partee (1995) review the more or less standard “hierarchy” of classes of
adjectives as a preliminary to arguing that arguments concerning the appropriateness of
prototype theory as a part of the account of the semantics of adjective-noun combinations
should be restricted to intersective adjectives. The hierarchy ranges from intersective
adjectives like carnivorous to privative adjectives like counterfeit, fake, and fictitious. The
same article makes some proposals for coercion of adjective meanings in context, driven by
certain general constraints, which help to explain a number of kinds of shifts and adjustments
that take place when adjective-noun combinations are interpreted in various kinds of
contexts. Some problem cases remained, especially the case of stone lion, where it seems that
the noun rather than the adjective shifts its meaning when faced with incompatibility of the
primary senses of each word. We’ll take up some of the responses to the stone lion problem
in Lecture 10, where we’ll also discuss a recent proposal of mine for a reanalysis of the
privative adjectives.
NZ3Adjbetter.doc
3
March 1, 2006
Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.4
3. Adjective classification
3.1. Meaning postulates for classes of adjectives
An adjective like carnivorous is intersective (Parsons: predicative), in that (4) holds for any
N.
||carnivorous N|| = ||carnivorous|| ∩ ||N||
(4)
But skillful is not, as shown by the invalid inference pattern in (5), familiar from the work of
Kamp, Parsons, Clark, and Montague cited in the introduction.
(5)
Premise: Francis is a skillful surgeon.
Premise: Francis is a violinist.
-----------------------------------------------Conclusion: Francis is a skillful violinist. INVALID
Skillful is not intersective, but it is subsective (Parsons: standard): (6) holds for any N.
Subsectivity: ||skillful N|| ⊆ ||N||
(6)
The adjectives former, alleged, counterfeit are neither intersective nor subsective.
(7)
(a) ||former senator|| ≠ ||former|| ∩ ||senator||
(b) ||former senator|| ⊄ ||senator||
Nonsubsective adjectives may either be “plain” nonsubsective (no entailments at all, no
meaning postulate needed), or privative, entailing the negation of the noun property. The
meaning postulate for privative adjectives is stated informally in (8).
(8)
||counterfeit N|| ∩ ||N|| = ∅
Additional examples of each type are given below.
(9)
(i) intersective: sick, carnivorous, blond, rectangular, French.
(ii) non-intersective but subsective: typical, recent, good, perfect, legendary.
(iiia) non-subsective and privative: would-be, past, spurious, imaginary, fictitious,
fabricated (in one sense), mythical (maybe debatable); there are prefixes with this property
too, like ex-, pseudo-, non-.
(iiib) plain non-subsective: potential, alleged, arguable, likely, predicted, putative,
questionable, disputed.
The conclusion drawn by Parsons, Kamp, Clark and Montague was that the simplest
general rule for interpretation of the combination of an adjective with a noun (or common
noun phrase: CNP) is the following: Adjectives are functions that map the (intensional)
semantic value of the CNP they combine with onto the semantic value of the ADJ + CNP
combination. That is, “The denotation of an adjective phrase is always a function from
properties to properties. (This was one of the proposals advanced by Kamp and Parsons.)”
(Montague 1970b, p.211 in Montague 1974)
NZ3Adjbetter.doc
4
March 1, 2006
Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.5
Meaning postulates specify various restrictions on these functions, characterizing various
subclasses of adjectives. "Semantic features" may be seen as labels for meaning postulates
which give them determinate content. Thus a lexical entry for an intersective adjective like
green might contain the “feature” INTERSECTIVE, or +INTERSECTIVE, which can be taken as
labelling a semantic property of the adjective, spelled out by a meaning postulate.
Meaning postulates for the subtypes listed above are spelled out in somewhat informal
terms below. P and Q are variables over properties; ADJ’ is a metalanguage variable over
adjective meanings.
(10)
Intersective adjectives: For each intersective adjective meaning ADJ’,
∃P∀x[ADJ’(Q)(x) ↔ P(x) & Q(x)]
(Alternatively, and probably preferably, intersective adjectives (and only those) can be
interpreted as one-place predicates. This automatically guarantees their intersectivity and
eliminates the need for a meaning postulate. Type-shifting rules of the sort described in
Partee (1995) will give them homonyms of functional type when needed.)
(11)
Subsective adjectives: For each subsective adjective meaning ADJ’,
∀x[ADJ’(Q)(x) → Q(x)]
The “plain” nonsubsective adjectives (alleged, possible) have no meaning postulate; this
class is "noncommittal": an alleged murderer may or may not be a murderer.
(12)
Privative adjectives: For each privative adjective meaning ADJ’,
∀xe[ADJ’(Q)(x) → ¬[Q(x)]]
The privative adjectives (fake, counterfeit) have a “negative” meaning postulate; a fake gun
is not a gun.
On this familiar classification, adjectives are seen as forming a hierarchy from
intersective to subsective to nonsubsective, with the privative adjectives an extreme case of
the nonsubsective adjectives.
There are of course many questions and disputes when it comes to assigning particular
adjectives to particular classes. Kamp (1975) added an important dimension to the discussion
in arguing that adjectives like tall, which at first sight seem to be non-intersective, are
actually intersective but context-dependent. Kamp’s analysis found linguistic support in
Siegel’s analysis of long-form and short-form adjectives in Russian (Siegel 1976a, 1976b).
There has been much further work on the semantics of adjectives in the intervening years,
and the context-dependence of interpretation of adjectives is central in the work of Klein
(1980) and most recently of Kennedy (1997).
Among many other debated points, one which has always been troubling, and to which
we will return in Lecture 10, is the question of whether an adjective or adjectivally used noun
like fake or toy is really privative. The problem can be illustrated by the tension between the
apparent truth of (13a) and the perfectly natural interpretability of (13b). (13a) supports the
standard treatment of privative adjectives; but (13b) should be anomalous if fake is really
privative: how can refer to “that thing” as a gun and then ask if it’s fake, i.e. not a gun?
(13)
a. A fake gun is not a gun.
b. Is that gun real or fake?
NZ3Adjbetter.doc
5
March 1, 2006
Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.6
3.2. Is tall intersective or subsective?.
In section 3.1 above we indicated that the inference pattern (5) was a test of whether an
adjective was intersective. By this test, it looks like vague adjectives like tall and young are
non-intersective:
(5’)
Premise: Tom is a tall 14-year-old.
Premise: Tom is a basketball player.
---------------------------------------------------------------------Conclusion: Tom is a tall basketball player. INVALID??
Does that mean that tall is not intersective? No; perhaps it is intersective but vague and
context-dependent. How can we tell the difference?
First argument. Keep the ADJ-N sequence constant but change other aspects of the
context. That can help to show whether it is the intension of the noun that is crucial.
(5’’)
a. My two-year-old son built a really tall snowman yesterday.
b. The linguistics students built a really tall snowman last weekend.
Further evidence that there is a difference between truly nonintersective subsective
adjectives like skillful and intersective but vague and context- dependent adjectives like tall
was noted by Siegel (1976b): the former occur with as-phrases, as in skillful as a surgeon,
whereas the latter take for- phrases to indicate comparison class: tall for an East coast
mountain. (An adjective can be nonintersective and also vague, and then one can use both an
as-phrase and a for-phrase: very good as a diagnostician for someone with so little
experience.)
4.
Conclusions
The adjective puzzles that we have been discussed so far and those we will discuss in
Lecture 10 are designed to illustrate several issues. One is the need to study lexical semantics
and principles of semantic composition together; decisions about either may have major
repercussions for the other. More importantly for this context, I have tried to show that while
contextually influenced meaning shifts pose challenges for compositionality, we can see that
compositionality plays an essential role in constraining the kinds of meaning shifts that take
place. We hold the principle of compositionality constant in working out (unconsciously)
what shifts our interlocutors may be signaling. In the extreme case we (like children) depend
on compositionality to figure out the meanings of novel words: if we can use contextual clues
to guess what the whole sentence means, we can then “solve” for the meaning of the
unknown word. Compositionality thus appears to be one of the most cognitively basic
principles in the realm of semantics.
References
Apresjan, Jurij D., Mel'chuk, Igor', and Zholkovsky, Aleksandr. 1969. Semantics and lexicography:
Towards a new type of unilingual dictionary. In Studies in Syntax and Semantics, ed. F. Kiefer, 133. Dordrecht: Reidel.
Apresjan, Jurij D. 1974. Leksičeskaja Semantika. [Lexical Semantics]. Moscow: Nauka.
Apresjan, Jurij D. 1986. Dejksis v leksike i grammatike i naivnaja model' mira [Deixis in lexicon and
grammar and the naive model of the world]. Semiotika i Informatika 28.
Apresjan, Jurij D. 1992. Lexical Semantics. A Guide to Russian Vocabulary. Ann Arbor: Karoma
Publishers.
NZ3Adjbetter.doc
6
March 1, 2006
Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.7
Apresjan, Jurij D. 1994. O jazyke tolkovanij i semantičeskix primitivax [On the language of lexical
explications and semantic primitives]. Izvestija Rossiskoj Akademii Nauk, Serija lit. i jazyka 53.
Apresjan, Jurij D. 1995. Izbrannye Trudy, Vol II: Integral'noe Opisanie Jazyka i Sistemnaja
Leksikografia [Integrated Description of Language and Systematic Lexicography]. Moscow:
Škola "Jazyki Russkoj Kultury".
Apresjan, Jurij D. 2000. Systematic Lexicography. (translated by K. Windle) Oxford: Oxford
University Press.
Bach, Emmon. 1986. Natural language metaphysics. In Logic, Methodology, and Philosophy of
Science VII, eds. Ruth Barcan Marcus, Georg J.W. Dorn and Paul Weingartner, 573-595.
Amsterdam: North-Holland.
Bennett, Michael. 1974. Some Extensions of a Montague Fragment of English, University of
California at Los Angeles: PhD. dissertation; distributed by Indiana University Linguistics Club.
Borschev, Vladimir, and Partee, Barbara H. 1998. Formal and lexical semantics and the genitive in
negated existential sentences in Russian. In Formal Approaches to Slavic Linguistics 6: The
Connecticut Meeting 1997, eds. Željko Boskovic, Steven Franks and William Snyder, 75-96. Ann
Arbor: Michigan Slavic Publications.
Clark, R.L. 1970. Concerning the Logic of Predicate Modifiers. Noûs 4:311-335.
Gouskova, Maria. 2000. The interaction of topic, focus and constituency in Russian. Ms. Amherst.
Heim, Irene. 1999. Class handout, spring seminar in semantics, MIT. Ms. Cambridge, MA.
Junghanns, Uwe. 2000. On rightward backgrounding. In FDSL 3, ed. Gerhild Zybatow, 329-343.
Kamp, Hans. 1975. Two theories about adjectives. In Formal Semantics of Natural Language, ed.
Edward L. Keenan, 123-155: Cambridge University Press.
Kamp, Hans, and Partee, Barbara. 1995. Prototype theory and compositionality. Cognition 57:129191.
Kennedy, Christopher. 1997. Projecting the Adjective, University of California Santa Cruz: Ph.D.
dissertation.
Klein, Ewan. 1980. A semantics for positive and comparative adjectives. Linguistics and Philosophy
4:1-45.
Lakoff, George. 1987. Women, Fire, and Dangerous Things. Chicago and London: The University of
Chicago Press.
Mehlhorn, Grit. 2000. Information structure of discontinuous constituents in Russian. In FDSL 3, ed.
Gerhild Zybatow, 344-352.
Mel'chuk, Igor A. 1974. Opyt teorii lingvisticheskix modelej tipa Smysl <==> Tekst. [Towards a
Theory of Linguistic Models of the Type "Meaning <==> Text"]. Moscow: Nauka.
Mel'chuk, Igor A. 1982. Lexical functions in lexicographic description. In BLS 8: Proceedings of the
Eighth Annual Meeting of the Berkeley Linguistics Society, 427-443. Berkeley, CA: Berkeley
Linguistics Society.
Mel'chuk, Igor A. 1988. Semantic description of lexical units in an explanatory combinatorial
dictionary: basic principles and heuristic criteria. International Journal of Lexicography 1:165188.
Mel'chuk, Igor A., and Zholkovsky, Aleksandr K. 1984. Explanatory Combinatorial Dictionary of
Modern Russian: Semantico Syntactic Study of Russian Vocabulary. Vienna: Wiener
Slawistischer Almanach.
Montague, Richard. 1970a. Universal grammar. Theoria 36:373-398. Reprinted in Montague 1974,
222-246.
Montague, Richard. 1970b. English as a Formal Language. In Linguaggi nella Società e nella
Tecnica, ed. Bruno Visentini et al., 189-224. Milan: Edizioni di Comunità. Reprinted in Montague
1974, 188-221.
Montague, Richard. 1973. The proper treatment of quantification in ordinary English. In Approaches
to Natural Language, eds. K.J.J. Hintikka, J.M.E. Moravcsik and P. Suppes, 221-242. Dordrecht:
Reidel. Reprinted in Montague 1974, 247-270; Reprinted in Portner and Partee, eds., 2002, 17-34.
Nowak, Anita. 2000. On split PPs in Polish. Ms. Amherst (unpublished General Paper, UMass.).
Parsons, Terence. 1970. Some problems concerning the logic of grammatical modifiers. Synthèse
21:320-334. Reprinted in Davidson and Harman 1972, 127-141.
NZ3Adjbetter.doc
7
March 1, 2006
Ling 310 The Structure of Meaning, Lecture 3
B.H. Partee, February 27, 2006 p.8
Partee, Barbara. 1984. Compositionality. In Varieties of Formal Semantics, eds. Fred Landman and
Frank Veltman, 281-312. Dordrecht: Foris. Reprinted in Partee, Barbara H. 2004.
Compositionality in Formal Semantics: Selected Papers by Barbara H. Partee. Oxford:
Blackwell Publishing, 153-181.
Partee, Barbara. 1995. Lexical semantics and compositionality. In An Invitation to Cognitive Science
(Second Edition). Volume 1: Language, eds. Lila Gleitman and Mark Liberman, 311-360.
Cambridge: MIT Press.
Partee, Barbara H. 1999. Semantics. In The MIT Encyclopedia of the Cognitive Sciences, eds. R.A.
Wilson and F.C. Keil, 739-742. Cambridge, MA: The MIT Press.
Partee, Barbara H. in press. Privative adjectives: subsective plus coercion. In Presuppositions and
Discourse, eds. Rainer Bäuerle, Uwe Reyle and Thomas Ede Zimmermann. Amsterdam:
Elsevier.
Siegel, Muffy. 1976a. Capturing the Russian adjective. In Montague Grammar, ed. Barbara H. Partee,
293-309. New York: Academic Press.
Siegel, Muffy E.A. 1976b. Capturing the Adjective, University of Massachusetts: Ph.D. dissertation.
Žolkovsky, Aleksandr, and Mel'chuk, Igor'. 1966. "O sisteme semantičeskogo sinteza. I: Stroenie
slovarja." ["On a system for semantic synthesis. I: Structure of the dictionary."]. Naučnotexničeskaja informacija 11:48-55.
Homework #2, Due March 6
Read Partee (1995) (the reading handed out in class) at least through page 325. Read the
Problems on pp 354-356.
(1)Answer the first problem, 11.1, p.354, (the “French teacher” problem) for any two
languages that you know and can find out about. Suggest a hypothesis about which meaning
will be expressed with a more ordinary, ‘unmarked’, adjective-noun combination in most
languages, and which meaning is more likely to be expressed in some other way. (Optional:
Do you have any hypothesis about why this is likely to be the case?)
(2) Problem 11.3, pp354-355. (classifying adjectives)
NZ3Adjbetter.doc
8
March 1, 2006