Learning and reasoning in large, structured, probabilistic worlds is at the heart of artificial intelligence. Markov decision processes have become the de facto standard in modeling and solving sequential decision making problems under uncertainty. Many efficient reinforcement learning and dynamic programming techniques exist that can solve such problems.
Until recently, the representational state-of-the-art in this field was based on propositional representations.

However, it is hard to imagine a truly general, intelligent system that does not conceive of the world in terms of objects and their properties and relations to other objects. To this end, this book studies lifting Markov decision processes, reinforcement learning and dynamic programming to the first-order (or, relational) setting. Based on an extensive analysis of propositional representations and techniques, a methodological translation is constructed from the propositional to the relational setting. Furthermore, this book provides a thorough and complete description of the state-of-the-art, it surveys vital, related historical developments and it contains extensive descriptions of several new model-free and model-based solution techniques.

/pdf/the-logic-of-adaptive-behavior-knowledge-representation-and-47husbqltg.pdf

The logic of adaptive behavior : knowledge representation and algorithms for the Markov decision process framework in first-order domains

Induction of recursive theories in the normal ILP setting is a difficult learning task whose complexity is equivalent to multiple predicate learning. In this paper we propose computational solutions to some relevant issues raised by the multiple predicate learning problem. A separate-and-parallel-conquer search strategy is adopted to interleave the learning of clauses supplying predicates with mutually recursive definitions. A novel generality order to be imposed on the search space of clauses is investigated, in order to cope with recursion in a more suitable way. The consistency recovery is performed by reformulating the current theory and by applying a layering technique, based on the collapsed dependency graph. The proposed approach has been implemented in the ILP system ATRE and tested on some laboratory-sized and real-world data sets. Experimental results demonstrate that ATRE is able to learn correct theories autonomously and to discover concept dependencies. Finally, related works and their main differences with our approach are discussed.

/pdf/learning-recursive-theories-in-the-normal-ilp-setting-5bj8e9ho5o.pdf

Learning Recursive Theories in the Normal ILP Setting

Learning is a crucial ability of intelligent agents. Rather than presenting a complete literature review, we focus in this paper on important issues surrounding the application of machine learning (ML) techniques to agents and multi-agent systems (MAS). In this discussion we move from disembodied ML over single-agent learning to full multi-agent learning. In the second part of the paper we focus on the application of Inductive Logic Programming, a knowledge-based ML technique, to MAS, and present an implemented framework in which multi-agent learning experiments can be carried out.

Machine learning and inductive logic programming for multi-agent systems

To compute a function such as a mapping from vertices to colors in the graph coloring problem, current practice in Answer Set Programming is to represent the function as a relation Among other things, this often makes the resulting program unnecessarily large when instantiated on a large domain The extra constraints needed to enforce the relation as a function also make the logic program less transparent In this paper, we consider adding functions directly to normal logic programs We show that the answer set semantics can be generalized to these programs straightforwardly We also show that the notions of loops and loop formulas can be extended, and that through program completion and loop formulas, a normal logic program with functions can be transformed to a Constraint Satisfaction problem

https://www.aaai.org/Papers/KR/2008/KR08-044.pdf

Answer set programming with functions

An Event Calculus program to control the navigation of a real robot was generated using Theory Completion techniques This is an application of ILP in the non-observational predicate learning setting This work utilized 1) extraction-case abduction; 2) the simultaneous completion of two, mutually related predicates; and 3) positive observations only learning Given time-trace observations of a robot successfully navigating a model office and other background information, Theory Completion was used to induce navigation control programs in the event calculus Such programs consisted of many clauses (up to 15) in two mutually related predicates This application demonstrates that abduction and induction can be combined to effect nonobservational multi-predicate learning

Using theory completion to learn a robot navigation control program

We focus on learning representations of dynamical systems that can be characterized by logic-based formalisms for reasoning about actions and change, where system's behaviors are naturally viewed as appropriate logical consequences of the domain's description. To this end, logic-based induction methods are adapted to identify the input/output behavior of a dynamical system corresponding to an environment. The study of dynamic domains is started with domains modelable with classical action theories and is progressively enhanced to manage more complex behaviors.

/pdf/learning-to-reason-about-actions-284x60kk93.pdf

Learning to reason about actions

In this work we reconsider the replacement of predicate-like notation by functional terms, using a similar syntax to Functional Logic Programming, but under a completely different semantic perspective. Our starting point comes from the use of logic programs for Knowledge Representation and Nonmonotonic Reasoning, especially under three well-known semantics for default negation: Clark’s completion, stable models and well-founded semantics. The motivation for introducing functions in this setting arises from the frequent occurrence of functional dependences in the representation of many domains. The use of functions allows us to avoid explicit axiomatization and provides a more compact representation by nesting functional terms. From a representational point of view, the most interesting introduced feature is the possibility of replacing default negation by the concept of default value of a function. In the paper, we explore this idea of functions with default values, providing adapted versions of the three mentioned semantics for the functional case, and equivalent translations into logic programs.

/pdf/logic-programs-with-functions-and-default-values-umzhym7ngm.pdf

Logic Programs with Functions and Default Values

In this work we further investigate the relation, first found by Truszczynski, between modal logic S4F and Default Logic (DL), analyzing some interesting properties and showing its application to other general non-monotonic formalisms. For comparison purposes, we start defining a subset of S4F we called Intuitionistic Default Logic (IDL), which consists in incorporating an additional set of propositional operators. These operators are translated into modal formulas using Godel's pattern for encoding Intuitionistic Logic into S4. Then, we prove that, under a particular models minimization policy, IDL generalizes Turner's Nested Default Logic (NDL), in the sense that the latter does not allow nesting or combining the rule conditional operator. This result is also used to show that strong equivalence of default theories can be reduced to a simple S4F equivalence test. Finally, we prove that IDL also generalizes Pearce's Equilibrium Logic, which encodes logic programs into the intermediate logic of Here-and-There.

/pdf/new-insights-on-the-intuitionistic-interpretation-of-default-3541kl9pgi.pdf

New insights on the intuitionistic interpretation of Default Logic

The relationship between Generalized Magnitudes (a Temporal Reasoning Scheme) and Discrete Event Systems Specifications is examined, revisiting a previous work of translation between both formalisms. As a result of this study, the Generalized Magnitudes Scheme is extended by adding autonomous activation — the system determines the next instant in which it must be re-evaluated. This new feature allows using the Generalized Magnitudes for representing and simulating Discrete Events models directly, which contributes several interesting representational properties. Finally, the computing process of the next activation instant is described.

David Lorenzo

Papers

Learning to reason about actions

Logic Programs with Functions and Default Values

New insights on the intuitionistic interpretation of Default Logic

Discrete Event Simulation in an Environment for Temporal Expert Systems

Using an ILP Algorithm to Learn Logic Programs for Reasoning about Actions.