This chapter describes how the SP System, meaning the SP Theory of Intelligence, and its realisation as the SP Computer Model, may promote transparency and granularity in AI, and some other areas of application. The chapter describes how transparency in the workings and output of the SP Computer Model may be achieved via three routes: 1) the program provides a very full audit trail for such processes as recognition, reasoning, analysis of language, and so on. There is also an explicit audit trail for the unsupervised learning of new knowledge; 2) knowledge from the system is likely to be granular and easy for people to understand; and 3) there are seven principles for the organisation of knowledge which are central in the workings of the SP System and also very familiar to people (eg chunking-with-codes, part-whole hierarchies, and class-inclusion hierarchies), and that kind of familiarity in the way knowledge is structured by the system, is likely to be important in the interpretability, explainability, and transparency of that knowledge. Examples from the SP Computer Model are shown throughout the chapter.

This paper describes problems in AI research and how the SP System may help to solve them. Most of the problems are described by leading researchers in AI in interviews with science writer Martin Ford, and reported by him in his book Architects of Intelligence. These problems, each with potential solutions via SP, are: how to overcome the divide between symbolic and non-symbolic kinds of knowledge and processing; eliminating large and unexpected errors in recognition; the challenge of unsupervised learning; the problem of generalisation, with under- and over-generalisation; learning from a single exposure or experience; the problem of transfer learning; how to create learning that is fast, economical in demands for data and computer resources; the problems of transparency in results and processing; problems in the processing of natural language; problems in the development of probabilistic reasoning; the problem of catastrophic forgetting; how to achieve generality across several aspects of AI. The SP System provides a relatively promising foundation for the development of artificial general intelligence.

In 'Winograd Schema' (WS) sentences like "The city councilmen refused the demonstrators a permit because they feared violence" and "The city councilmen refused the demonstrators a permit because they advocated revolution", it is easy for adults to understand what "they" refers to but can be difficult for AI systems. This paper describes how the SP System -- outlined in an appendix -- may solve this kind of problem of interpretation. The central idea is that a knowledge of discontinuous associations amongst linguistic features, and an ability to recognise such patterns of associations, provides a robust means of determining what a pronoun like "they" refers to. For any AI system to solve this kind of problem, it needs appropriate knowledge of relevant syntax and semantics which, ideally, it should learn for itself. Although the SP System has some strengths in unsupervised learning, its capabilities in this area are not yet good enough to learn the kind of knowledge needed to interpret WS examples, so it must be supplied with such knowledge at the outset. However, its existing strengths in unsupervised learning suggest that it has potential to learn the kind of knowledge needed for the interpretation of WS examples. In particular, it has potential to learn the kind of discontinuous association of linguistic features mentioned earlier.

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to information compression, couched in terms of non-mathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics has grown out of an extensive programme of research developing the "SP Theory of Intelligence" and its realisation in the "SP Computer Model", a system in which a generalised version of ICMUP -- the powerful concept of SP-multiple-alignment -- plays a central role. These ideas may be seen to be part of a "Big Picture" comprising six areas of interest, with information compression as a unifying theme. The paper describes the close relation between mathematics and information compression, and describes examples showing how variants of ICMUP may be seen in widely-used structures and operations in mathematics. Examples are also given to show how the mathematics-related disciplines of logic and computing may be understood as ICMUP. There are many potential benefits and applications of these ideas.

This paper describes a novel approach to software engineering derived from the "SP Theory of Intelligence" and its realisation in the "SP Computer Model". Despite superficial appearances, it is shown that many of the key ideas in software engineering have counterparts in the structure and workings of the SP system. Potential benefits of this new approach to software engineering include: the automation or semi-automation of software development, with support for programming of the SP system where necessary; allowing programmers to concentrate on 'world-oriented' parallelism, without worries about parallelism to speed up processing; support for the long-term goal of programming the SP system via written or spoken natural language; reducing or eliminating the distinction between 'design' and 'implementation'; reducing or eliminating operations like compiling or interpretation; reducing or eliminating the need for verification of software; reducing the need for validation of software; no formal distinction between program and database; the potential for substantial reductions in the number of types of data file and the number of computer languages; benefits for version control; and reducing technical debt.

This paper describes a roadmap for the development of the "SP Machine", based on the "SP Theory of Intelligence" and its realisation in the "SP Computer Model". The SP Machine will be developed initially as a software virtual machine with high levels of parallel processing, hosted on a high-performance computer. The system should help users visualise knowledge structures and processing. Research is needed into how the system may discover low-level features in speech and in images. Strengths of the SP system in the processing of natural language may be augmented, in conjunction with the further development of the SP system's strengths in unsupervised learning. Strengths of the SP system in pattern recognition may be developed for computer vision. Work is needed on the representation of numbers and the performance of arithmetic processes. A computer model is needed of "SP-Neural", the version of the SP Theory expressed in terms of neurons and their inter-connections. The SP Machine has potential in many areas of application, several of which may be realised on short-to-medium timescales.

This paper describes how the "SP Theory of Intelligence" with the "SP Computer Model", outlined in an Appendix, may throw light on aspects of commonsense reasoning (CSR) and commonsense knowledge (CSK), as discussed in another paper by Ernest Davis and Gary Marcus (DM). In four main sections, the paper describes: 1) The main problems to be solved; 2) Other research on CSR and CSK; 3) Why the SP system may prove useful with CSR and CSK 4) How examples described by DM may be modelled in the SP system. With regard to successes in the automation of CSR described by DM, the SP system's strengths in simplification and integration may promote seamless integration across these areas, and seamless integration of those area with other aspects of intelligence. In considering challenges in the automation of CSR described by DM, the paper describes in detail, with examples of SP-multiple-alignments. how the SP system may model processes of interpretation and reasoning arising from the horse's head scene in "The Godfather" film. A solution is presented to the 'long tail' problem described by DM. The SP system has some potentially useful things to say about several of DM's objectives for research in CSR and CSK.

This article provides a brief introduction to the "Theory of Intelligence" and its realisation in the "SP Computer Model". The overall goal of the SP programme of research, in accordance with long-established principles in science, has been the simplification and integration of observations and concepts across artificial intelligence, mainstream computing, mathematics, and human learning, perception, and cognition. In broad terms, the SP system is a brain-like system that takes in "New" information through its senses and stores some or all of it as "Old" information. A central idea in the system is the powerful concept of "SP-multiple-alignment", borrowed and adapted from bioinformatics. This the key to the system's versatility in aspects of intelligence, in the representation of diverse kinds of knowledge, and in the seamless integration of diverse aspects of intelligence and diverse kinds of knowledge, in any combination. There are many potential benefits and applications of the SP system. It is envisaged that the system will be developed as the "SP Machine", which will initially be a software virtual machine, hosted on a high-performance computer, a vehicle for further research and a step towards the development of an industrial-strength SP Machine.

The "SP theory of intelligence", with its realisation in the "SP computer model", aims to simplify and integrate observations and concepts across AI-related fields, with information compression as a unifying theme. This paper describes how abstract structures and processes in the theory may be realised in terms of neurons, their interconnections, and the transmission of signals between neurons. This part of the SP theory -- "SP-neural" -- is a tentative and partial model for the representation and processing of knowledge in the brain. In the SP theory (apart from SP-neural), all kinds of knowledge are represented with "patterns", where a pattern is an array of atomic symbols in one or two dimensions. In SP-neural, the concept of a "pattern" is realised as an array of neurons called a "pattern assembly", similar to Hebb's concept of a "cell assembly" but with important differences. Central to the processing of information in the SP system is the powerful concept of "multiple alignment", borrowed and adapted from bioinformatics. Processes such as pattern recognition, reasoning and problem solving are achieved via the building of multiple alignments, while unsupervised learning -- significantly different from the "Hebbian" kinds of learning -- is achieved by creating patterns from sensory information and also by creating patterns from multiple alignments in which there is a partial match between one pattern and another. Short-lived neural structures equivalent to multiple alignments will be created via an inter-play of excitatory and inhibitory neural signals. The paper discusses several associated issues, with relevant empirical evidence.

This article describes existing and expected benefits of the "SP theory of intelligence", and some potential applications. The theory aims to simplify and integrate ideas across artificial intelligence, mainstream computing, and human perception and cognition, with information compression as a unifying theme. It combines conceptual simplicity with descriptive and explanatory power across several areas of computing and cognition. In the "SP machine" -- an expression of the SP theory which is currently realized in the form of a computer model -- there is potential for an overall simplification of computing systems, including software. The SP theory promises deeper insights and better solutions in several areas of application including, most notably, unsupervised learning, natural language processing, autonomous robots, computer vision, intelligent databases, software engineering, information compression, medical diagnosis and big data. There is also potential in areas such as the semantic web, bioinformatics, structuring of documents, the detection of computer viruses, data fusion, new kinds of computer, and the development of scientific theories. The theory promises seamless integration of structures and functions within and between different areas of application. The potential value, worldwide, of these benefits and applications is at least $190 billion each year. Further development would be facilitated by the creation of a high-parallel, open-source version of the SP machine, available to researchers everywhere.