This volume is a collection of essays related to the work of Professor Yuriy Vasilievich Ivlev, a distinguished Russian logician and philosopher renowned for his expertise in many-valued and modal logics. Notably, his groundbreaking work on quasi-matrices for logics, now recognized as non-deterministic matrices and non-deterministic semantics, emerged in the 1970s. From a philosophical standpoint, Ivlev’s research delves into the formal analysis of indeterminacy, offering a logical framework to understand how sequences of indeterminate events can yield determinate outcomes. The volume follows two complementary lines of research. Firstly, it serves as a platform for the exploration and discussion of Ivlev’s seminal contributions to the algebraic characterization of both normal and non-normal modal logics, aimed at making these insights accessible to an international audience. Secondly, it features contributions from esteemed logicians and philosophers worldwide, offering diverseperspectives on the logical analysis of indeterminacy. This comprehensive volume will appeal to scholars and researchers in logic, philosophy, and mathematics who are engaged in the study of many-valued and modal methodologies for modeling situations of indeterminacy.

This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all.

This book contains a selection of papers presented at the International Workshop Machine Learning, Meta-Reasoning and Logics held in Hotel de Mar in Sesimbra, Portugal, 15-17 February 1988. All the papers were edited afterwards. The Workshop encompassed several fields of Artificial Intelligence: Machine Learning, Belief Revision, Meta-Reasoning and Logics. The objective of this Workshop was not only to address the common issues in these areas, but also to examine how to elaborate cognitive architectures for systems capable of learning from experience, revising their beliefs and reasoning about what they know. Acknowledgements The editing of this book has been supported by COST-13 Project Machine Learning and Knowledge Acquisition funded by the Commission o/the European Communities which has covered a substantial part of the costs. Other sponsors who have supported this work were Junta Nacional de lnvestiga~ao Cientlfica (JNICT), lnstituto Nacional de lnvestiga~ao Cientlfica (INIC), Funda~ao Calouste Gulbenkian. I wish to express my gratitude to all these institutions. Finally my special thanks to Paula Pereira and AnaN ogueira for their help in preparing this volume. This work included retyping all the texts and preparing the camera-ready copy. Introduction 1 1. Meta-Reasoning and Machine Learning The first chapter is concerned with the role meta-reasoning plays in intelligent systems capable of learning. As we can see from the papers that appear in this chapter, there are basically two different schools of thought.

Formal methods are a robust approach for problem solving. It is based on logic and algebraic methods where problems can be formulated in a way that can help to find an appropriate solution. This book shows the basic concepts of formal methods and highlights modern modifications and enhancements to provide a more robust and efficient problem solving tool.

Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems.

Since the first edition was published two years ago, much has been done on extend­ ing the work done on SMART to address new and important areas [3-5,54,79,80, 108-110,116,118-120,122]. In this second edition, we have revised, updated and corrected the existing text and added three new chapters. These chapters provide a broader coverage of the fie1d of agents, and show in more detail how the specific framework described can be used to examine other areas. In Chapter 6, we use the concepts of discovery to apply the framework to autonomous interaction in multi­ agent systems; in Chapter 10 we use it for considering normative agents and sys­ tems; and in Chapter 11 we describe work on an implementation and development environment.

The computer programming language Prolog is quickly gaining popularity throughout the world. Since Its beginnings around 1970. Prolog has been chosen by many programmers for applications of symbolic computation. including: D relational databases D mathematical logic D abstract problem solving D understanding natural language D architectural design D symbolic equation solving D biochemical structure analysis D many areas of artificial Intelligence Until now. there has been no textbook with the aim of teaching Prolog as a practical programming language. It Is perhaps a tribute to Prolog that so many people have been motivated to learn It by referring to the necessarily concise reference manuals. a few published papers. and by the orally transmitted 'folklore' of the modern computing community. However. as Prolog is beginning to be Introduced to large numbers of undergraduate and postgraduate students. many of our colleagues have expressed a great need for a tutorial guide to learning Prolog. We hope this little book will go some way towards meeting this need.

The major goal of this book is to present the techniques of top-down program design and verification of program correctness hand-in-hand. It thus aims to give readers a new way of looking at algorithms and their design, synthesizing ten years of research in the process. It provides many examples of program and proof development with the aid of a formal and informal treatment of Hoare's method of invariants. Modem widely accepted control structures and data structures are explained in detail, together with their formal definitions, as a basis for their use in the design of correct algorithms.

This book constitutes the refereed proceedings of the 32nd International Conference on Inductive Logic Programming, ILP 2023, held in Bari, Italy, during November 13–15, 2023. The 11 full papers and 1 short paper included in this book were carefully reviewed and selected from 18 submissions. They cover all aspects of learning in logic, multi-relational data mining, statistical relational learning, graph and tree mining, learning in other (non-propositional) logic-based knowledge representation frameworks, exploring intersections to statistical learning and other probabilistic approaches.

In the 1930s, mathematical logicians studied the notion of "effective comput­ ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.