On the Representation of Deadlines in a Rental Agreement

Many agreements and contracts contain deadlines. Because deadlines combine time and obligations, they are naturally studied by a combination of temporal logic with deontic logic [2]. A deadline, that ϕ should occur before δ, can be expressed as a formula which involves the ‘until’-operator: OBL(ϕ Uδ). However, such a characterisation does not in-dicate what will happen after the deadline. Since deadlines can have different functions, it is likely that several notions of deadline can be distinguished. Recently, we have pre-sented a conceptual analysis of deadlines, based on the following parameters: whether we are dealing with an achievement or a maintenance obligation, persistence of the oblig-ation after the deadline, the choice of modal operator (permission or obligation) and the presence of an explicit or implicit sanction [3]. Temporal Modal Defeasible Logic For each of these parameters template formulas are provided, in a logic called Temporal Modal Defeasible logic (TMDL). TMDL is an ex-tension of Defeasible Logic [1] to capture deontic modalities (OBL,PERM) and aspects of time, in particular intervals. For example, OBLpay: [t,max] expresses that there is obligation to pay from t until indefinitely. Crucial is the distinction between strict rule