Project Objectives

One of the key open questions of artificial intelligence concerns probabilistic logic learning, i.e. the integration of probabilistic reasoning, with first order logic representations and machine learning. Throughout this description of work the term logic refers to the predicate calculus or first order logic.

Let us first clarify what we mean by probabilistic logic learning by investigating its underlying constituents. The term probabilistic in our context refers to the use of probabilistic representations and reasoning mechanisms grounded in probability theory, such as Bayesian networks, hidden Markov models and stochastic grammars. Such representations have been successfully used across a wide range of applications and have resulted in a number of robust models for reasoning about uncertainty. Application areas include genetics, bioinformatics, computer vision, speech recognition and understanding, diagnostic and troubleshooting, information retrieval, software debugging, data mining and user modelling.

The term logic in the present description of work refers to representations based on the predicate calculus (i.e., first order logic) such as those studied within the field of computational logic. The primary advantage of using such representations is that it allows one to elegantly represent complex situations involving a variety of objects as well as relations among the objects. Consider e.g. the problem of building a logical troubleshooting system of a set of computers. Computers are complex objects which are themselves composed of several complex objects. Furthermore, assume that even though the overall structure of the computers can be the same, their individual components can be highly di erent. Such situations can be elegantly modelled using relational or first order logic representations. E.g., we could use the relation ram(r1, c1) to specify that computer c1 has a RAM component of type r1, and cpu(p2, c1) and cpu(p3, c1) to denote that c1 is a multi-processor machine with two cpu s p2 and p3. In addition to these base (or extensional) relations, one can also add virtual (or intensional) relations to describe generic knowledge about the domain. E.g., consider the rule

multiprocessor(C) :- cpu(P1,C), cpu(P2, C), P1 =\= P2.

which defines the concept of a multi-processor machine (as a machine that possesses two di erent cpu s). Representing the same information employing a propositional logic would require one to specify for each machine a separate model.

The term learning in the context of probabilistic logic refers to deriving the di erent aspects of a model in a probabilistic logic on the basis of data. Typically, one distinguishes various learning algorithms on the basis of the given data (fully or partially observable data) or on the aspect being learned (the parameters of the probabilistic representation or its logical structure). The motivation for learning is that it is often easier to obtain data for a given application domain and learn the model than to build the model using traditional knowledge engineering techniques.

So, probabilistic logic learning aims at combining its three underlying constituents: learning and probabilistic reasoning within first order logic representations.