Satisfiability for First-order Logic as a Non-Modal Deontic Logic

In modal deontic logics, the focus is on inferring logical consequences, for example inferring whether or not an obligation O mail, to mail a letter, logically implies O [mail  burn] ,an obligation to mail or burn the letter. Here I present an alternative approach in which obligations are sentences (such as mail) in first-order logic (FOL), and the focus is on satisfying those sentences by making them true in some best model of the world. To facilitate this task and to make it manageable in this alternative approach, models are defined by a logic program (LP) extended by means of action assumptions (A). The resulting combination of FOL, LP and A is a variant of abductive logic programming (ALP). 1 Goal satisfaction in FOL In the abductive logic programming (ALP) approach of [8, 10], candidate assumptions (A), representing actions and other “abducibles”, and logic programs (LP), representing an agent’s beliefs, are combined with first-order logic (FOL), representing an agent’s goals. However, this characterisation of ALP is potentially misleading, because it fails to identify the primary role of goals, and the supporting role of beliefs and assumptions in helping to make goals true. Here is a more abstract characterisation, which is formulated entirely in terms of FOL, and does not mention A or LP at all: A goal satisfaction problem is a tuple G, M0, W where: G is a set of sentences in FOL, representing goals. M0 is a classical FOL model-theoretic structure, representing a partial history of the world. W is a set of classical FOL model-theoretic structures, representing alternative extensions of M0. MW satisfies a goal satisfaction problem G, M0, W if and only if