Luis Lamb

This book provides an invaluable overview of the reach of logic. It provides reference to some of the most important, well-established results in logic, while at the same time offering insight into the latest research issues in the area. It also has a balance of theory and practice, containing essays in the areas of modal logic, intuitionistic logic, logic and language, nonmonotonic logic and logic programming, temporal logic, logic and learning, combination of logics, practical reasoning, logic and artificial intelligence, abduction, theorem proving and goal-directed reasoning. It will be invaluable reading for researchers and graduate students in logic and computer science, and a fabulous source of inspiration for research students in search of a topic for a PhD in logic and theoretical computer science.

K. Broda, Dov M. Gabbay, Alessandra Russo and LuÍs C. Lamb argue that though the many families of logic may seem to differ in their logical nature, it is possible to provide them with a unifying logical framework whenever their semantics is axiomatizable in first-order logic. They provide such a framework based on the labeled deductive system methodology, and demonstrate how it works in such families as normal modal logics, conditional logics of normality, the modal logic of elsewhere, the multiplicative fragment of substructural linear logic, and Lukasiewicz fuzzy logic.

Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computational model for argumentation and (ii) neural networks can be used to combine argumentation, quantitative reasoning and statistical learning. At the same time, non-standard logic models of argumentation started to emerge. In this paper, we propose a connectionist cognitive model of argumentation that accounts for both standard and non-standard forms of argumentation. The model is shown to be an adequate framework for dealing with standard and non-standard argumentation, including joint-attacks, argument support, ordered attacks, disjunctive attacks, meta-level attacks, self-defeating attacks, argument accrual and uncertainty. We show that the neural cognitive approach offers an adequate way of modelling all of these different aspects of argumentation. We have applied the framework to the modelling of a public prosecution charging decision as part of a real legal decision making case study containing many of the above aspects of argumentation. The results show that the model can be a useful tool in the analysis of legal decision making, including the analysis of what-if questions and the analysis of alternative conclusions. The approach opens up two new perspectives in the short-term: the use of neural networks for computing prevailing arguments efficiently through the propagation in parallel of neuronal activations, and the use of the same networks to evolve the structure of the argumentation network through learning (e.g. to learn the strength of arguments from data).

Humans are often extraordinary at performing practical reasoning. There are cases where the human computer, slow as it is, is faster than any artificial intelligence system. Are we faster because of the way we perceive knowledge as opposed to the way we represent it? The authors address this question by presenting neural network models that integrate the two most fundamental phenomena of cognition: our ability to learn from experience, and our ability to reason from what has been learned. This book is the first to offer a self-contained presentation of neural network models for a number of computer science logics, including modal, temporal, and epistemic logics. By using a graphical presentation, it explains neural networks through a sound neural-symbolic integration methodology, and it focuses on the benefits of integrating effective robust learning with expressive reasoning capabilities. The book will be invaluable reading for academic researchers, graduate students, and senior undergraduates in computer science, artificial intelligence, machine learning, cognitive science and engineering. It will also be of interest to computational logicians, and professional specialists on applications of cognitive, hybrid and artificial intelligence systems.