PDL-based framework for reasoning about actions [chapter]

Giuseppe Giacomo, Maurizio Lenzerini
1995 Lecture Notes in Computer Science  
Propositional Dynamic Logics (PDL's) provide a suitable formal framework for modeling actions and reasoning about them. However, the basic language of PDL's lack several features that are important for a sophisticated treatment of actions. In this paper, we present a new logic that is obtained by enriching the basic PDL with powerful modeling constructs that allow us to represent determinism and nondeterminisms, concurrency, hierarchies, mutual exclusion, backward execution, and non-execution
more » ... actions. We demonstrate, by m e a n s o f examples, the expressive p o wer of the formalism. In particular, we s h o w that although nonmonotonicity is not generally captured by PDL's, our logic is perfectly suited for exploiting monotonic solutions to the frame problem. Finally, w e establish that the proposed formalism is decidable, and that the basic reasoning problems are EXPTIME-complete. 2 The logic DIFR Formulae in the logic DIFRare of two s o r t s : action formulae and state formulae. Action Formulae describe properties, by means of boolean operators, of atomic actions -i.e., actions that cannot be broken in sequences of smaller actions. The abstract syntax of action formulae is as follows: ::= P j any j 1^ 2 j 1 _ 2 j : where P denotes a primitive action, and any denotes a special atomic action that can be thought of as \the most general atomic action". Observe that an atomic action denoted by an action formulae is composed, in general, by a set of primitive actions intended to be executed in parallel.
doi:10.1007/3-540-60437-5_10 fatcat:twki64offfcwnghkpepwd5tqvi