Dov Gabbay

We introduce \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}}$$\end{document} -ranked preferential structures and combine them with an accessibility relation. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}}$$\end{document} -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}}$$\end{document} -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.

This eighteenth volume of the acclaimed Handbook of Philosophical Logic includes many contributors who are among the most famous leading figures of applied philosophical logic of our time. Coverage includes deontic logic, practical reasoning, homogeneous and heterogeneous logical proportion, and talmudic logic. Overall, it will appeal to students, practitioners, and researchers looking for an authoritative resource in these areas. The contributors first explore models in terms of dynamic logics for information-driven agency. The paradigm they use is dynamic-epistemic logics for knowledge and belief and their current extensions to the statics and dynamics of agents’ preferences. Next, in the presentation of preference based agency, coverage examines a large number of themes, including interactive social agents and scenarios with long term patterns emerging over time. From here, the book moves on to offer an introduction to homogeneous and heterogeneous logical proportions. Readers will also learn more about the general challenge that the problem of formalizing practical reasoning presents to logical theory. The contributors survey the existing resources that might contribute to the development of such a formalization. They conclude that, while a robust, adequate logic of practical reasoning is not yet in place, the materials for developing such a logic are now available. The last chapter explores topics that deal with the logic of Jewish law and the logic of the Talmud. This includes obligations and prohibitions in Talmudic deontic logic, the handling of loops in Talmudic logic, Temporal Talmudic logic, and quantum states and disjunctive attacks in Talmudic logic. The Talmudic logic system presented are also exported to general logic and to Artificial Intelligence.

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration.

As one of the basic tasks in natural language processing (NLP), named entity recognition (NER) is an important basic tool for downstream tasks of NLP, such as information extraction, syntactic analysis, machine translation and so on. The internal operation logic of the current name entity recognition model is black-box to the user, so the user has no basis to determine which name entity makes more sense. Therefore, a user-friendly explainable recognition process would be very useful for many people. In this paper, we propose a novel interpretable method, BTPK (Binary Talmudic Public Announcement Logic model), to help users understand the internal recognition logic of the name entity recognition tasks based on Talmudic Public Announcement Logic. BTPK model can also capture the semantic information in the input sentences, that is, the context dependency of the sentence. We observed the public announcement of BTPK presents the inner decision logic of Bidirectional Recurrent Neural Networks (BRNNs), and the explanations obtained from a BTPK model show us how BRNNs essentially handle NER tasks.

This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator–prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster–Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005.

The traditional Dung networks depict arguments as atomic and study the relationships of attack between them. This can be generalised in two ways. One is to consider various forms of attack, support, feedback, etc. Another is to add content to nodes and put there not just atomic arguments but more structure, e.g. proofs in some logic or simply just formulas from a richer language. This paper offers to use temporal and modal language formulas to represent arguments in the nodes of a network. The suitable semantics for such networks is Kripke semantics. We also introduce a new key concept of usability of an argument. This is the beginning of a continuing research for adding contents to the nodes of an argumentation network. This research will allow us to address notions like ‘what does it exactly mean for a node to attack another’ or ‘what does it mean for a network to be consistent’ or ‘can we give proper proof rules to manipulate networks’, and more.

Stone-walling dialogues are exercises in structured non-cooperation. It is true that dialogue participants need to cooperate with one another and in ways sufficient to make possible the very dialogue they are now having. Beyond that there is room for non-cooperation on a scale that gives great offence to what we call the Goody Two-Shoes Model of argument. In this paper, we argue that non-cooperation dialogues have perfectly legitimate objectives and that in relation to those objectives they need not be considered at all subpar to conversations that brim with sunny amity.Two categories of stone-walling non-cooperation dialogues are here examined. They are called MindClosed and NoEngage. They are exemplified by the following cases:1. Hostile Police Interrogation2. Judicial Cross-Examination3. Department Store Complaints Management4. Lakatosian Science5. Gödel's First Incompleteness Proof

The purpose of this paper is to communicate some developments in what we call the new logic. In a nutshell the new logic is a model of the behaviour of a logical agent. By these lights, logical theory has two principal tasks. The first is an account of what a logical agent is. The second is a description of how this behaviour is to be modelled. Before getting on with these tasks we offer a disclaimer and a warning. The disclaimer is that although the new logic is significantly different from it, we have no inclination to see the new logic as a rival of mathematical logic. We do not advocate the displacement of, e.g. model theory, but rather its supplementation or adaptation. The warning is that, whereas mathematical logic must eschew psychologism, the new logic cannot do without it. The fuller story of the new logic must eschew psychologism, the new logic cannot do without it. The fuller story of the new logic is part of our book, The Reach of Abduction, scheduled to appear in 2001 or early 2002