Interval semantics

Dowty (1979) bases his theory on the following premises:

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i. Philosophical insight from the research of Aristotle, Kenny (1963), Reyle (1949) and Vendler (1967).

ii. Lexical decomposition analysis of generative semantics (Lakoff 1965, McCawley 1968).

iii. Formal theories of truth-conditional and model theoretic semantics.

Dowty bases his aspectual classification on two main criteria: change and possession of, or lack of, a culmination point [±definite]. His aspectual classes are shown in figure 2 below:

Figure 2

Dowty uses a fifth criterion - agency - in his classification. This criterion is

perpendicular with the other aspectual properties in figure 2 above and it splits the four classes into two:

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i. Agentive (activities, accomplishments).

ii. Non-agentive (states, achievements).

However, agentivity cuts across the different classes above. There are

accomplishments that are non-agentive as well as achievements that permit forms that are related to agency and control. Agency therefore is not per se a criterion for

aspectual classification (Smith 1991, Verkuyl 1993 and Pianesi and Varzi 2000).

In figure 2, the bifurcation between Momentary and Interval represents the Static versus non-static classification between events and states and that between definite

Verbal predicates

Momentary Interval

States (As in habitual use of verbs in all classes)

No change Change

Other

states Indefinite definite

Activities Singular (absence of an event)

Complex

(subsidiary causal events that bring about the resultative state

Achievement Accomplishment

and indefinite represents the telic/non-telic distinction. Lastly, the singular/complex bifurcation represents agency/non agency distinction in [+definite] events. In figure 1 the one I propose, the first two are represented by the bifurcation between events and states for the former and between transition and no transition for the later. Agency is not represented in figure 1 for reasons which will be discussed immediately below. In addition, in figure 1 a classification is made along duration/no duration distinction.

Dowty (1972) proposes a reductionist approach whereby the different aspectual properties of the various kinds of verbs can be explained by postulating a single homogeneous class of predicates: stative predicates plus three or four sentential operators and connectives. Statives are used as the base for all other derivatives because they can be judged “true or false of an individual by reference to the state of the world at only a single movement of time while other classes of verbs require

“information” about more than one point in time and in some cases more than one possible world” (1979:71). Thus activities, accomplishments and achievements have stative predicates as basic structures together with three sentential operators DO, BECOME and CAUSE and the combinatory apparatus of intensional logic. He uses evidence from adverbial modification to buttress his classification.⁴⁰ The following examples are representative of the logical formulas of the four classes (1979:123) (24)

i. Simple states Vn (a1, …, an)

(John knows the answer).

ii. Simple activities Do a1 ([Vn (a1, … , an) ] ) (John is walking).

iii. Non-agentive [[BECOME Ø] CAUSE [BECOME ψ]]

accomplishment where ∅ and ψ are stative sentences (The door opening causes the lamp to fall).

iv. (Non-intensional [[DO(α1, [πn , (α1,…, αn )]) CAUSE (BECOME agentive Accomplishments [ρm (β1,…,β2)]]].

(John broke the window).

v. Simple Achievements BECOME [Vn (a1, …, an)]

Here Vn is an n- place predicate and a1, …, an its arguments.

(John discovered the solution).

Pianesi and Vassi (2000) mention two problems with this analysis with respect to their translation in intensional logic. Firstly, causative verbs and their paraphrases with the causative verb cause are not always synonymous. For example, following Dowty’s analysis, the sentence John opened the door is supposed to entail the logical formula for non-intentional agentive accomplishments, as well as, the sentence John caused the door to become open. They point out that this however is not the case. The logical formula does not entail direct causation and is therefore not a sufficient

condition for the truth condition of the sentence. Secondly quoting Chierchia and McConnell-Ginet (1990) they assert that data from adverbial modification do not directly support Dowty’s decomposition analysis. They observe for example that verbs like clean are not judged intuitively to have internal modifier interpretations.

(25) John caused the jacket to be clean again.

(26) John cleaned the jacket again.

A situation where John bought a new jacket and the first time the jacket got dirty, he cleaned it, is only expressed by (25) and not by (26). Yet, on Dowty’s decomposition analysis both sentences should be true of this situation. Dowty (1979:97) addresses the above contention. The operator CAUSE is an abstract element and need not be considered identical with the English surface verb cause. The surface verb cause might contain other abstract predicates beside CAUSE in its underlying representation or it might differ from cause in its presupposition.

Turning now to the operator BECOME, Dowty defines it from the point of view of interval semantics. According to him (1977:49) it is extremely doubtful that “the

result-state of an accomplishment comes to be true at a single moment rather than an interval of time”. Achievements are composed of two parts of a transition

proposition: ¬∅ T ∅. Following Benneth and Partee (1978), Dowty (1977, 1979), in order to explain what happens between the states corresponding to ∅ and ¬∅, defines BECOME in terms of intervals. BECOME is defined as:

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[[BECOME Ø]] M,I g = 1 iff

i. For some interval jΣ I containing the lower bound of i, [[Ø]] M,I g =0.

ii. For some interval kΣ I containing the upper bound of i, [[Ø]] M,k g =1.

iii. There is no non-empty i^'⊂i such that a and b hold for i^' and I.

A sentence like Mary walked to Rome is true with respect to the interval i iff at i Mary was not in Rome during interval j and at k Mary is in Rome. The gap between not be in Rome (the lower boundary of j in i) and be in Rome (the upper boundary of k in i) is bridged by BECOME together with the stipulation in (27iii):

Condition (27i) is designed to limit the truth of ∅ to the smallest interval to which the change of state has taken place. Dowty points out that this stipulation is too strong because as long as Ø is bivalent, then [BECOME Ø ] can only be true at an interval no larger than a moment (the process of becoming must be shortened to just two moments: the lower boundary j and the upper boundary k). However condition (27iii) can be interpreted as a felicity condition on assertions based on Grices conversational maxims making it possible for truth value gaps between j and k).Thus semantic, pragmatic and discourse information become relevant for an adequate aspectual description of verbal predicates.