Distributed First Order Logic

Distributed First Order Logic (DFOL) has been introduced more than ten years ago with the purpose of formalising distributed knowledge-based systems, where knowledge about heterogeneous domains is scattered into a set of interconnected modules. DFOL formalises the knowledge contained in each module by means of first-order theories, and the interconnections between modules by means of special inference rules called bridge rules. Despite their restricted form in the original DFOL formulation, bridge rules have influenced several works in the areas of heterogeneous knowledge integration, modular knowledge representation, and schema/ontology matching. This, in turn, has fostered extensions and modifications of the original DFOL that have never been systematically described and published. This paper tackles the lack of a comprehensive description of DFOL by providing a systematic account of a completely revised and extended version of the logic, together with a sound and complete axiomatisation of a general form of bridge rules based on Natural Deduction. The resulting DFOL framework is then proposed as a clear formal tool for the representation of and reasoning about distributed knowledge and bridge rules

A Robust Logical and Computational Characterisation of Peer-to-Peer Database Systems

In this paper we give a robust logical and computational characterisation of peer-to-peer (p2p) database systems. We first define a precise model-theoretic semantics of a p2p system, which allows for local inconsistency handling. We then characterise the general computational properties for the problem of answering queries to such a p2p system. Finally, we devise tight complexity bounds and distributed procedures for the problem of answering queries in few relevant special cases

On Projectivity in Markov Logic Networks

Markov Logic Networks (MLNs) define a probability distribution on relational structures over varying domain sizes. Many works have noticed that MLNs, like many other relational models, do not admit consistent marginal inference over varying domain sizes. Furthermore, MLNs learnt on a certain domain do not generalize to new domains of varied sizes. In recent works, connections have emerged between domain size dependence, lifted inference and learning from sub-sampled domains. The central idea to these works is the notion of projectivity. The probability distributions ascribed by projective models render the marginal probabilities of sub-structures independent of the domain cardinality. Hence, projective models admit efficient marginal inference, removing any dependence on the domain size. Furthermore, projective models potentially allow efficient and consistent parameter learning from sub-sampled domains. In this paper, we characterize the necessary and sufficient conditions for a two-variable MLN to be projective. We then isolate a special model in this class of MLNs, namely Relational Block Model (RBM). We show that, in terms of data likelihood maximization, RBM is the best possible projective MLN in the two-variable fragment. Finally, we show that RBMs also admit consistent parameter learning over sub-sampled domains