We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial intelligence, therefore establishing it as a rigorous scientific discipline. We also relate to our own work in incremental machine learning and philosophy of complexity.

We present here a view on abstraction originating from the relation between formulas in a partially ordered language L and their extension on a set of instances W . In Formal Concept Analysis, this relation is materialized as a lattice G . Particular self-maps on either L or the powerset P ( W) are known to ensure structure-preserving reductions of the lattice G and have been shown to be in one to one correspondence with abstractions , defined subsets of either L or P ( W) closed under union. We investigate specifically extensional abstractions (subsets of P ( W) . Such an abstraction comes down to a change in granularity: extensions are now considered as union of abstract instances , that is, union of predefined subsets of instances. The main contribution of the paper is the investigation of the class of (non normal) monotonic modal logics whose semantics relies on such abstractions, and that we call abstract modal logics .

Learning to use an object as a tool requires understanding what goals it helps to achieve, the properties of the tool that make it useful and how the tool must be manipulated to achieve the goal. We present a method that allows a robot to learn about objects in this way and thereby employ them as tools. An initial hypothesis for an action model of tool use is created by observing another agent accomplishing a task using a tool. The robot then refines its hypothesis by active learning, generating new experiments and observing the outcomes. Hypotheses are updated using Inductive Logic Programming. One of the novel aspects of this work is the method used to select experiments so that the search through the hypothesis space is minimised.

Cognitive systems with human-level intelligence must dis­play a wide range of abilities, including reasoning about the beliefs of others, hypothetical and future situations, quanti­fiers, probabilities, and counterfactuals. While each of these deals in some way with reasoning about alternative states of reality, no single knowledge representation framework deals with them in a unified and scalable manner. As a conse­quence it is difficult to build cognitive systems for domains that require each of these abilities to be used together. To enable this integration we propose a representational framework based on synchronizing beliefs between worlds. Using this framework, each of these tasks can be reformu­lated into a reasoning problem involving worlds. This demonstrates that the notions of worlds and inheritance can bring significant parsimony and broad new abilities to knowledge representation.

This article proposes a suite of design decisions for the overall design of an Artificial Intelligence, i.e., a software system that exhibits intelligence in the spirit of the early days of A.I. research. The key aspects of the proposal are: (1) The identification of the A.I. system as a software individual that has the properties of integrity and persistence; (2) The construction of a software platform that integrates aspects of incremental programming languages and systems as well as of operating systems, with aspects that are intrinsic to knowledge-based artificial intelligence; (3) The use of a representation language that builds on essential aspects of S-expressions, Lisp, logic and extended set theory, but which is used both as a vehicle for software and as a publication language e.g. in lecture notes; (4) The identification of actions and aggregates of actions as first-class citizens in the representation language and as an important type of data object in the software system. The article also describes the Leonardo software platform, its representation language, its educational resources and its knowledgebase library which is one implementation of these proposed design decisions. Finally it makes a proposal concerning the research paradigm for this research area.

An important form of learning involves acquiring skills that let an agent achieve its goals. While there has been considerable work on learning in planning, most approaches have been sensitive to the representation of domain context, which hurts their generality. A learning mechanism that constructs skills effectively across different representations would suggest more robust behavior. In this paper, we present a novel approach to learning hierarchical task networks that acquires conceptual predicates as learning proceeds, making it less dependent on carefully crafted background knowledge. The representation acquisition procedure expands the system's knowledge about the world, and leads to more rapid learning. We show the effectiveness of the approach by comparing it with one that doesnot change domain representation.

We present a system capable of automatically solving combinatorial logic puzzles given in (simplified) English. It involves translating the English descriptions of the puzzles into answer set programming(ASP) and using ASP solvers to provide solutions of the puzzles. To translate the descriptions, we use a lambda-calculus based approach using Probabilistic Combinatorial Categorial Grammars (PCCG) where the meanings of words are associated with parameters to be able to distinguish between multiple meanings of the same word. Meaning of many words and the parameters are learned. The puzzles are represented in ASP using an ontology which is applicable to a large set of logic puzzles.

Model checking is a promising technology, which has been applied for verification of many hardware and software systems. In this paper, we introduce the concept of model update towards the development of an automatic system modification tool that extends model checking functions. We define primitive update operations on the models of Computation Tree Logic (CTL) and formalize the principle of minimal change for CTL model update. These primitive update operations, together with the underlying minimal change principle, serve as the foundation for CTL model update. Essential semantic and computational characterizations are provided for our CTL model update approach. We then describe a formal algorithm that implements this approach. We also illustrate two case studies of CTL model updates for the well-known microwave oven example and the Andrew File System 1, from which we further propose a method to optimize the update results in complex system modifications.

Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational structure that can be naturally described in terms of objects and relations among them. Two contributions are presented. First, the paper develops First Order Decision Diagrams (FODD), a new compact representation for functions over relational structures, together with a set of operators to combine FODDs, and novel reduction techniques to keep the representation small. Second, the paper shows how FODDs can be used to develop solutions for RMDPs, where reasoning is performed at the abstract level and the resulting optimal policy is independent of domain size (number of objects) or instantiation. In particular, a variant of the value iteration algorithm is developed by using special operations over FODDs, and the algorithm is shown to converge to the optimal policy.

Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as differential equations. Quantitative modelling works best when the structure of the model (i.e., the form of the equations) is known; and the primary concern is one of estimating the values of the parameters in the model. For complex biological systems, the model-structure is rarely known and the modeler has to deal with both model-identification and parameter-estimation. In this paper we are concerned with providing automated assistance to the first of these problems. Specifically, we examine the identification by machine of the structural relationships between experimentally observed variables. These relationship will be expressed in the form of qualitative abstractions of a quantitative model. Such qualitative models may not only provide clues to the precise quantitative model, but also assist in understanding the essence of that model. Our position in this paper is that background knowledge incorporating system modelling principles can be used to constrain effectively the set of good qualitative models. Utilising the model-identification framework provided by Inductive Logic Programming (ILP) we present empirical support for this position using a series of increasingly complex artificial datasets. The results are obtained with qualitative and quantitative data subject to varying amounts of noise and different degrees of sparsity. The results also point to the presence of a set of qualitative states, which we term kernel subsets, that may be necessary for a qualitative model-learner to learn correct models. We demonstrate scalability of the method to biological system modelling by identification of the glycolysis metabolic pathway from data.