Claes Strannegård

An anthropomorphic method for number sequence problems

Number sequence problems appear frequently in IQ tests, where the task is to extrapolate finite sequences of integers. This paper presents a computational method for solving number sequence problems appearing in IQ tests. The assumption that these problems are solvable by humans is actively exploited to keep the computational complexity manageable. The method combines elements of artificial intelligence and cognitive psychology and is referred to as anthropomorphic because it makes use of a model of human reasoning. This model features a set of cognitive resources, a repertoire of patterns that encode integer sequences, and a notion of bounded computation for decoding patterns. The model facilitates the search for patterns matching a given integer sequence by quickly discarding many patterns on the grounds that they are too demanding to decode. The computational method was implemented as a computer program called Asolver and then tested against the programs Mathematica and Maple. On the number sequence problems of the IQ test PJP, Asolver scored above IQ 140, whereas the other programs scored below IQ 100.

Bounded kolmogorov complexity based on cognitive models

Computable versions of Kolmogorov complexity have been used in the context of pattern discovery [1]. However, these complexity measures do not take the psychological dimension of pattern discovery into account. We propose a method for pattern discovery based on a version of Kolmogorov complexity where computations are restricted to a cognitive model with limited computational resources. The potential of this method is illustrated by implementing it in a system used to solve number sequence problems. The system was tested on the number sequence problems of the IST IQ test [2], and it scored 28 out of 38 problems, above average human performance, whereas the mathematical software packages Maple, Mathematica, and WolframAlpha scored 9, 9, and 12, respectively. The results obtained and the generalizability of the method suggest that this version of Kolmogorov complexity is a useful tool for pattern discovery in the context of AGI.

An anthropomorphic method for progressive matrix problems

Progressive matrix problems are frequently used in modern IQ tests. In a progressive matrix problem, the task is to identify the missing element that completes the pattern of a pictorial matrix. We present a method for solving progressive matrix problems. The method is not limited to problems that are on the multiple choice format, which makes it potentially useful for solving real-world pattern discovery problems that do not come with predefined answer alternatives. The method is anthropomorphic in the sense that it uses certain problem solving strategies that were reported by high-achieving human solvers. We also describe a computer program implementing this method. The computer program was tested on the sets C, D, and E of Ravens Standard Progressive Matrices test and it produced correct solutions for 28 of the 36 problems considered. This score corresponds roughly to an IQ of 100. Finally, we conclude that it is possible to solve progressive matrix problems without analyzing potential answer alternatives and discuss some implications of this finding.

A cognitive architecture based on dual process theory

This paper proposes a cognitive architecture based on Kahnemans dual process theory [1]. The long-term memory is modeled as a transparent neural network that develops autonomously by interacting with the environment. The working memory is modeled as a buffer containing nodes of the long-term memory. Computations are defined as processes in which working memory content is transformed according to rules that are stored in the long-term memory. In this architecture, symbolic and subsymbolic reasoning steps can be combined and resource-bounded computations can be defined ranging from formal proofs to association chains.

Reasoning About Truth in First-Order Logic

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment.

Bounded Cognitive Resources and Arbitrary Domains

When Alice in Wonderland fell down the rabbit hole, she entered a world that was completely new to her. She gradually explored that world by observing, learning, and reasoning. This paper presents a simple system Alice in Wonderland that operates analogously. We model Alices Wonderland via a general notion of domain and Alice herself with a computational model including an evolving belief set along with mechanisms for observing, learning, and reasoning. The system operates autonomously, learning from arbitrary streams of facts from symbolic domains such as English grammar, propositional logic, and simple arithmetic. The main conclusion of the paper is that bounded cognitive resources can be exploited systematically in artificial general intelligence for constructing general systems that tackle the combinatorial explosion problem and operate in arbitrary symbolic domains.

Emotional Concept Development

Artificial emotions of different varieties have been used for controlling behavior, e.g. in cognitive architectures and reinforcement learning models. We propose to use artificial emotions for a different purpose: controlling concept development. Dynamic networks with mechanisms for adding and removing nodes are more flexible than networks with a fixed topology, but if memories are added whenever a new situation arises, then these networks will soon grow out of proportion. Therefore there is a need for striking a balance that ideally ensures that only the most useful memories will be formed and preserved in the long run. Humans have a tendency to form and preserve memories of situations that are repeated frequently or experienced as emotionally intense strongly positive or strongly negative, while removing memories that do not meet these criteria. In this paper we present a simple network model with artificial emotions that imitates these mechanisms.

A General System for Learning and Reasoning in Symbolic Domains

We present the system O ⋆ that operates in arbitrary symbolic domains, including arithmetic, logic, and grammar. O ⋆ can start from scratch and learn the general laws of a domain from examples. The main learning mechanism is a formalization of Occam’s razor. Learning is facilitated by working within a cognitive model of bounded rationality. Computational complexity is thereby dramatically reduced, while preserving human-level performance. As illustration, we describe the learning process by which O ⋆ learns elementary arithmetic. In the beginning, O ⋆ knows nothing about the syntax or laws of arithmetic; by the end, it has constructed a theory enabling it to solve previously unseen problems such as “what is 67*8?” and “which number comes next in the sequence 8,11,14?”.

A new AI evaluation cosmos: Ready to play the game?

We report on a series of new platforms and events dealing with AI evaluation that may change the way in which AI systems are compared and their progress is measured. The introduction of a more diverse and challenging set of tasks in these platforms can feed AI research in the years to come, shaping the notion of success and the directions of the field. However, the playground of tasks and challenges presented there may misdirect the field without some meaningful structure and systematic guidelines for its organization and use. Anticipating this issue, we also report on several initiatives and workshops that are putting the focus on analyzing the similarity and dependencies between tasks, their difficulty, what capabilities they really measure and ultimately on elaborating new concepts and tools that can arrange tasks and benchmarks into a meaningful taxonomy.

Integrating Symbolic and Sub-symbolic Reasoning

This paper proposes a way of bridging the gap between symbolic and sub-symbolic reasoning. More precisely, it describes a developing system with bounded rationality that bases its decisions on sub-symbolic as well as symbolic reasoning. The system has a fixed set of needs and its sole goal is to stay alive as long as possible by satisfying those needs. It operates without pre-programmed knowledge of any kind. The learning mechanism consists of several meta-rules that govern the development of its network-based memory structure. The decision making mechanism operates under time constraints and combines symbolic reasoning, aimed at compressing information, with sub-symbolic reasoning, aimed at planning.