The Logic of Aspect, Aktionsart and Argument Structure
In this paper it is argued that lexical entries of verbs are composed of primitive predicates and arguments that fully
predetermine the projection of their syntactic tree. The theory used is a combination of Montague semantics and
generative syntax, which has recently become known as the concept of 'transparent LF'.
The argument grid of verbs not only includes thematic arguments, but also implicit arguments of time, event
and, in the case of resultatives, resultative predicates, which are either lexically bound or must be saturated in
syntax. If classes of verbs are systematically differentiated according to the Aktionsarten punktual/ durative and to
the lexical conditions of their argument structure (which includes also resultativity as a verbal character), and to the
potential of aspectual interaction with perfectivity/ imperfectivity, there are exactly 17 types of possible verbal
predicates. Those we will classify ontologically on the grounds of compositional predicate logic. We assume the
following system that is an amendment to those proposed by VENDLER (1967) or EHRICH (1992):
(1)
The elements of our formalism are:
 Temporal quantification (cf. FABRICIUS-HANSEN 1991) and event arguments (cf. DAVIDSON 1967)
(2)
a) Mary was pregnant: t[ t>t° & pregnant'(t,Mary') ]
b) Mary laughed: te[ tt° & AT(e,t) & lach'(e,Maria') ]
( t is argument of the lexeme function)
( e is the argument, t and e are in relation)
 durative vs. punctual: intervals
(3)
Interval
t1,t2  i  t(t1tt2  t  i)
 event time (t*), reference time (t) and speech time (t°) (cf. REICHENBACH 1947):
(4)
a) When Joe told a joke, Mary laughed.
b) t*ie1e2x[ t* i & it° & AT(e1,i) & tell'(e1,Joe,x) & joke'(x) & AT(e2,t*) & laugh'(e2,Mary) ]
 aspectual operators (modified from CANN 1993, 252ff)
(5)
a) [Pf]M,g,i =1  [φ]M,g,i* =1 & t(t  i*)  t'(i* t')
b) [Impf]M,g,i = 1  [φ]M,g,i* = 1 & j( ji* )

(6)
truth intervals (simplified notation):
a) BE BORN: xi*t[ t  i* & live'(i*,x)]
b) DIE: xi*t[ i* t & live'(i*,x)]
c) LIVE: xi*j[ ji* & live'(i*,x)] (i* may be bigger than reference time)
 lexical entries with saturated arguments (vgl. ENGELBERG 2000, 106f ) yield argument reduction in
syntax:
(7)
a) eat (transitive): yxe[ eat'(i*,e,x,y) ]
b) eat (intransitive): xey[ eat'(i*,e,x,y) ]
( lexical binding)
 lexical entries of verb classes in predicate logic: times and predicate variables as implicit arguments
(cf. V. STECHOW 1993, 58ff):
(8)
a) x[squint'(x)]
(property)
b) xi*j[ji&live'(i*,x)]
(state)
c) yxet*[AT(e,t*)&result'(e,x,y)]
d) xei*j[ji*&AT(e,i*)&blow'(e,x)]
(incidence)
(proceeding)
e) xet*[AT(e,t*)&cough'(e,x)]
(Act1)
f) yxet*[AT(e,t*)&kiss'(e,x,y)]
(Act2)
g) xei*j[ji*&AT(e,i*)&sleep'(e,x)]
(activity1)
h) yxei*j[ji*&AT(e,i*)&observe'(e,x,y)]
(activity2)
i) xtt*eP+res[AT(e,t*)&explode'(e,x)&t*t&P(t,x)]
(result)
j) xtt*ei*jP+res[ji*&AT(e,i*)&age'(e,x)&(t*t)i*&P(t,x)]
(process)
k) xtei*P+res[i*t&AT(e,i*)&sink'(e,x)&P(t,x)]
(development)
l) xtt*eP+res[AT(e,t*)&land'(e,x)&t*t&P(t,x)]
(achievement1)
m) xtt*ei*jP+res[ji*&AT(e,i*)&train'(e,x)&(t*t)i*&P(t,x)]
n) xtei*P+res[i*t&AT(e,i*)&moult'(e,x)&P(t,x)]
o) yxtet*P+res[AT(e,t*)&discover'(e,x,y)&t*t&P(t,y)]
(action1)
(accomplishment1)
(achievement 2)
p) yxtt*ei*jP+res[ji*&AT(e,i*)&frighten'(e,x,y)&t*i*&t*t&P(t,y)]
q) ytxei*P+res[i*t&AT(e,i*)&build'(e,x,y)&P(t,y)]
(action 2)
(accomplishment 2)
 The implicit resultative predicates are of course defining the semantics of the primary predicate.
Therefore they may be better formalised like:
(9)
a) xtt*e[ AT(e,t*) & PATIENT(e,x) & t*t & exploded'(t,x) ]: to explode
b) xtt*ei*j[ ji* & t*i* & AT(e,i*) & PATIENT(e,x) & t*t & old(er)'(t,x) ]: to age
c) xtei*[ i*t & AT(e,i*) & PATIENT(e,x) & alive'(t,x) ] : to die
d) etc.
 Achievements, actions and accomplishments with patient objects are causative. They imply results,
processes or developments. Therefore they can be decomposed into subevents. Of course this
implies separate conditions on aspect and aktionsart.
(10)
a) P+resytiekt*xei[AT(ei,t*)&CAUSE(ei,x,ek)&SHOT(ei)&AGENT(ei,x)&t*i
&AT(ek,i)&MOVE(ek,y)&THEME(ek,y)ti&PGOAL(t,y)] : to shoot
b) P+resytt*i*ekxeij[ji*&AT(ei,i*)&CAUSE(ei,x,ek)&AGENT(ei,x)&AT(ek,i*)&
MOVE(ek,y)&THEME(ek,y)& (t*t)i* &PGOAL(t,y)] : to move
c) P+resyteki*xei[AT(ei,t)&CAUSE(ei,x,ek)& AGENT(ei,x) & t  i* & AT(ek,i*) & MOVE(ek,y)
&THEME(ek,y) & PSOURCE(t,y)] : to fetch
 -Konversion means saturation of the argument grid through projection into syntax. The following
formulae are in fact LFs. Every bound variable and/ or term corresponds to a terminal node in a
syntactic tree.
(11)
a) t*eiekiyt[t*t°&AT(ei,t*)&CAUSE(ei,Joe',ek)&SHOT(ei)&t*i&AT(ek,i)
&MOVE(ek,the-ball')&ti&OVER(t,the-ball', the-goal')]
b) i*jeiekt [i*t°& ji*&AT(ei,i*)&CAUSE(ei,Joe',ek)&AT(ek,i*)&MOVE(ek,his-body')& (t*t)i* & AT(t,hisbody', the-field')]
c) t*eii*ekt [t*t°& AT(ei,t*)&CAUSE(ei,Joe',ek)&t* i*& AT(ek,i*)&MOVE(ek,Jim')&t*t&AT(t,Jim',theairport')]
(12)
a) Joe shot the ball over the goal.
b) Joe moved his body over the field.
c) Joe fetched Jim from the airport.
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