Quanti cation in Dynamic Semantics

In dynamic semantics three styles of quanti cation have been proposed that can be seen to involve two di erent ways of interpreting free and quanti ed variables: Variables as denoting single partial objects; Variables as ranging over a number of alternative total objects. I will show that the rst view leads to problems of underspeci cation and the second to problems of overspeci cation. I will propose a new style of dynamic quanti cation in which variables are interpreted in a way which avoids these problems: Variables as ranging over a number of alternative de nite objects (concepts). By relativizing quanti cation to ways of conceptualizing the domain, we avoid the cardinality problems which arise if quanti cation is over concepts rather than objects. Background and Motivation In dynamic semantics, sentences characterize transitions across a space of information states. Information states are generally de ned as sets of possibilities (here world-assignment pairs) and meanings describe shifts from states to states: updating with sentences may lead to smaller states in which possibilities have been eliminated, or to richer ones in which new discourse items have been added. Atoms, for example, yield smaller states resulting from eliminating those world-assignment pairs that do not satisfy them. Existential sentences lead to richer states: 9x adds x and selects a number of possible values for it; the fact that in the output state(s) x is de ned means that recurrences of x in later sentences can refer anaphorically. Information about variables is generally modelled in one of the two following ways: 1. Variables are interpreted as single partial objects. The introduction of new items is de ned in terms of global extensions that involve adding fresh variables and assigning them as possible values all elements of the universe. 2. Variables are taken to range over a number of total objects. The introduction of a new item is de ned in terms of individual extensions that lead to the states resulting from adding a variable and assigning it as value a single element of the universe. 1. Global Extension w1 w2 x