On the Equivalence Between the L 1 Action Language and Partial Actions in Transaction Logic Mart´ ın Rezk 1 and Michael Kifer 2 1 KRDB Research Center, Free University of Bozen-Bolzano, Bolzano, Italy rezk@inf.unibz.it 2 Department of Computer Science, Stony Brook University, NY 11794, U.S.A. kifer@cs.stonybrook.edu Abstract. Transaction Logic with Partially Defined Actions (TR PAD ) is an ex- pressive formalism for reasoning about the effects of actions and for declarative specification of state-changing transactions. The action language L1 is a well- known formalism to describe changing domains and for reasoning about actions. The purpose of this paper is to compare these two formalisms and identify their similarities and points of divergence in order to better understand their modeling and reasoning capabilities. We provide a sound reduction of a large fragment of L1 to TR PAD , and show that this reduction is complete with respect to the LP em- bedding of L1. We also explore how action planning is modeled in both languages and discuss the relationship to other languages for representing actions. 1 Introduction Designing agents that can reason about actions has been a long-standing target in AI. Of particular interest are agents whose underlying mechanisms are founded on solid logical foundations. A number of sophisticated logical theories for such agents have been developed over the years, including A[?], L 1 [1], C [?], ALM[?]. Unfortunately, most of such languages have their weak points along with the strong ones, and neither is sufficient as a logical foundation for agents. Another area where action theories are important is Semantic Web Services, since it is necessary to reason about the effects of actions in order to discover, contract, and enact such services automatically [2,5]. Recently, another powerful language for actions, based on partially defined actions in Transaction Logic (abbr., TR PAD ), was proposed [?]. This language is based on a very different logical paradigm than the aforesaid languages, and it is an interesting challenge to understand the relative expressive power of these languages. In this paper we identify and compare the modeling and reasoning capabilities of TR PAD and L 1 . We chose L 1 because it is a powerful language that can serve as a good representative of the family of action languages mentioned earlier. However, we also briefly discuss the relation between TR PAD and action languages C and ALM. After introducing the languages, we compare them on a number of examples and then prove the equivalence between subsets of both languages. However, it is the sym- metric difference of these languages that is perhaps most interesting. Throughout this paper we investigate that difference using the following running example.