Distributed Abductive Reasoning with Constraints (Extended Abstract) Jiefei Ma Alessandra Russo Krysia Broda Emil Lupu Department of Computing, Imperial College London, United Kingdom, SW7 2AZ {jm103,ar3,kb,ecl1}@doc.ic.ac.uk ABSTRACT Abductive inference has many known applications in multi- agent systems. However, most abductive frameworks rely on a centrally executed proof procedure whereas many of the application problems are distributed by nature. Confi- dentiality and communication overhead concerns often pre- clude transmitting all the knowledge required for centralised reasoning. We present in this paper a novel multi-agent ab- ductive reasoning framework underpinned by a flexible and extensible distributed proof procedure that permits collabo- rative abductive reasoning with constraints between agents over decentralised knowledge. Categories and Subject Descriptors H.4 [Information Systems Applications]: Miscellaneous General Terms Algorithms Keywords Multi-agent Reasoning, Abductive Logic Programming 1. INTRODUCTION Abductive reasoning is a powerful inference mechanism that can generate conditional proofs. The combination of Abduction and Logic Programming (ALP) [5] has many known applications, such as planning, scheduling, cognitive robotics, medical diagnosis and policy analysis [3]. However, most abductive frameworks [6, 4, 7] rely on a centrally exe- cuted proof procedure whereas many of the application prob- lems are distributed by nature. Confidentiality and commu- nication overhead concerns often preclude transmitting all the knowledge required for centralised reasoning. Recently, ALIAS [1] and DARE [8] have shown how to distribute ab- ductive computation in a collaborative system. However, their distributed proof procedures, which are based on the well-known Kakas-Mancarella procedure [6], do not support constructive negation [10] and cannot compute non-ground conditional proofs. Hence they cannot be used for applica- Cite as: Proc. of 9th Int. Conf. on Autonomous Agents and Multia- gent Systems (AAMAS 2010) c tions such as scheduling and planning involving time and cost, which require constraint processing [11]. In order to overcome this limitation, we propose DAREC, a distributed abductive logic programming framework un- derpinned by a general and customisable proof procedure that permits collaborative abductive reasoning with con- straint processing between decentralised (computational logic) agents. The collaborative reasoning can be seen as a state rewriting process, where the reasoning state, initially con- taining just the query, is exchanged between the agents. Agents rewrite the state during their local inference by adding relevant (non-ground) assumptions and (dynamically gener- ated) constraints that can then be checked for global consis- tency. The answer can then be extracted from the final state when the overall reasoning succeeds. DAREC can be applied to both closed and open multi-agent systems, i.e. whether the set of agents is fixed or changes dynamically. 2. FRAMEWORK Let L be a predicate logic language consisting of three disjoint sets of predicates: abducible, non-abducible and con- straint. Each agent in DAREC has a unique identifier id and can be modeled with an abductive framework F id = 〈Π, AB, I〉, where Π is a constraint logic program called the background knowledge, AB is a set of abducible predicates, and I is a set of integrity constraints of the form ← B where B is a conjunction of literals over L. Given a set Σ of such agents, the DAREC framework F dis is 〈Σ, Π dis , AB, I dis 〉, where (a) Π dis = S i∈Σ Πi, (b) I dis = S i∈Σ , and (c) AB = ABi = ABj for any i, j ∈ Σ, which implies that all the agents agree on the same set of abducibles. Although semantically Π dis and I dis are the unions of all the agent background knowledge and integrity constraints respectively, they are not physically centralised. Given a query Q (a conjunction of literals over L called the goals), a DAREC answer w.r.t. F dis is a pair 〈Δ,θ〉, such that: (i) Δ is a set of abducible atoms, θ is a set of variable substitutions; (ii) Π dis ∪ Δ | = Qθ; and (iii) Π dis ∪ Δ | = I dis . Thus, condition (iii) defines the requirement of global consistency – the answer is consistent with the overall agent integrity constraints. This is different from ALIAS where only local consistency is guaranteed, i.e. the answer is consistent with each agent’s integrity constraints locally. 3. PROOF PROCEDURE The DAREC proof procedure assumes that agents (1) ex- ecute the proof procedure docilely when requested, and (2) can find out what non-abducibles are known by (i.e. defined in) other agents. The former ensures that the agents are 1381 1381-1382