In my Temporality book (Bittner 2014), I propose that every language has one or two grammatical paradigms of obligatory TAM categories (tense, aspect, or mood) interpreted as a centering system that keeps track of top-ranked discourse referents. Grammatical tense keeps track of top-ranked times; grammatical aspect, of top-ranked eventualities (events or states); and grammatical mood, of top-ranked modalities. The proposed theory predicts six types of languages: tense-based, aspect-based, mood-based, tense-aspect-based, aspect-mood-based, or tense-mood-based.
This proposal is implemented in a framework where ranked discourse referents are represented in Update with Centering (UC), a typed dynamic logic with rank-based anaphora. Logical UC representations are derived by directly compositional rules of Categorial Grammar (CG). The combined framework is called CG.UC (i.e. CG composition of UC representations).
- English (Germanic: Indo-European): CG.UC fragment (see Bittner 2014, Ch. 8)
- Mandarin (Sino-Tibetan): interlinear texts; sample texts in UC; topic states in Mandarin discourse; CG.UC fragment (see Bittner 2014, Ch. 10)
- Kalaallisut (Eskimo-Aleut): interlinear texts; fieldwork on mood and evidentiality; CG.UC fragment (see Bittner 2014, Ch. 11)
- Polish (Slavic, Indo-European): CG.UC fragment (see Bittner 2014, Ch. 9)