The authors of the LIV assume a dichotomy between telic verbs (terminated: for example, *leh₂p- 'to light up') and atelic verbs (ongoing: for example, *bʰeh₂- 'to shine') in early stages of Proto-Indo-European. Before the daughter languages split off, aspect emerged as a new grammatical category.
Telic verbs were interpreted as aorist forms, and the missing present was formed with various suffixes (for example, *leh₂p-: *l̥h₂p-sḱé-) and the nasal infix (*l̥h₂-né-p-), all of which are supposed to come from old grammatical forms of uncertain meaning.
Atelic verbs were interpreted as present forms, and the missing aorist was formed with the suffix -s-, yielding the sigmatic aorist.
This hypothesis is used to explain various phenomena:
Some verbs in Indo-European languages form root presents (Latindūcō 'I pull, I lead', from PIE*deu̯k-, *duk-) and derived sigmatic aorists (perfect forms in Latin: dūxī 'I have pulled, I have led', pronounced dūksī, from *déu̯k-s-).
Other verbs form root aorists (Latin vīcī 'I have won', pronounced vīkī, from *wei̯k-, *wik-) and derived present forms (vincō 'I win', from *wi-n-k-, with nasal infix).
For many PIE verbs, various present forms can be reconstructed without discernible differences in meaning (like *l̥h₂-né-p- and *l̥h₂p-sḱé- above, both forms have attested reflexes in IE languages: Greekλάμπω 'I shine' and Proto-Celtic *laske- 'to shine, burn', respectively).
In addition to the present and the aorist, the following aspects are assumed:
reconstructed stems with their reflexes in the daughter languages,
extensive footnotes (with references, remarks on alternative and dubious reconstructions, etc.),
the page number of the corresponding IEW entry.
The book includes
a regressive root index,
an index of reconstructed primary stems, sorted by aspect and formation rule,
an index of reflexes in the daughter languages, sorted by language.
Reception and criticism
Seebold claims insufficient evidence for roots reconstructed from a single daughter language. Helmut Rix insists in the preface to the second edition that the assessment of the evidence should be left to the reader.
Seebold also criticises some of the conjectured meanings. Rix calls this criticism basically legitimate.
Meier-Brügger tentatively calls the LIV's aspect hypothesis “adequate and capable of consensus” (adäquat und konsensfähig), without agreeing on all of the details of the analysis.
Fortson calls the LIV “[v]ery useful and up-to-date – though in various places controversial”, but does not elaborate on the controversial places.
Ringe states that the theories in Rix (what he terms the “Cowgill-Rix verb”) largely reflect current consensus, but implies that some of his phonological reconstructions may go beyond the consensus (in terms of being insufficiently “conservative”).