Logic, Language and Legal Science: Are We Lagging Behind?

The central theme of this article is that modern notions of logic, deriving from computer logics and also from the language and logic movement in philosophy, provide a sound basis for legal science and hence for legal writing, law practice and legal education. Scepticism about legal formalism largely derives from the fact that the term logic is still taken to mean the syllogistic logic of Aristotle. Modern notions of logic, generally referred to as formalism or formal studies, view knowledge in general and science in particular in terms of game theory, applying word, number letter and iconic games to data in order to achieve certain objectives. Formal games are old in the law; the forms of action at common law have produced several simple games, for instance the AND game and the OR game which continue to function in legal argument. Game theory can also supply valuable formal tools apt for use in legal education, legal writing and law practice. These include branching diagrams (algorithms) and the decisional logics used in business and in medical practice. Examples of the use of such methods in legal writing are given in the appendices

A Syntactic Approach to Rationality in Games

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994).rationality, common belief, rationalizability, dominated strategies, game logic, frame characterization

Logic and Rationality

Logic aims at truth, or more accurately, at deriving some truths from other truths. But why are we interested in truth in the first place? Surely one reason is that relying on truth makes it easier to make better choices. One could think of Game theory as a tool which bridges the gap between logic and rationality. Decision theory - or single agent game theory tells us when to make the best choice in a game of us against nature. But nature has no desire to further or frustrate our efforts. Nature is mysterious but not malign. Things change when there are other agents involved. Then the best thing for us to do will depend on what they do. And they will think the same. Issues like common knowledge and rationalizability will then arise

Open research for diffusion of open digital memories at Web 2.0/3.0

This paper suggests an experimental perspective of Open Research, understood as a process of deconstruction of knowledge about society that leads to its reconstruction, archiving and dissemination in the form of Open Digital Memories. This posture was developed within the Project Public Communication of Art: the Case of Global / Local Art Museums, at the University of Lisbon. The project was funded by Foundation for Science and Technology, and produced 6 books and 8 sites, among other final results. Researching and memorizing may be pursuited through an open style that includes the production and reception of investigation by both the researcher and the common citizen. This may involve multiple shared tasks: questioning the social, organization and critique of sources and data, co-participation in the use of methods, public discussions on work in progress and on research results. For this aim, Open Research must articulate Social Sciences and Humanities to New Media, specially across digital social networks, both at Web 2.0 (the Reading/Writing Internet) and at Web 3.0 (the so-called Semantic Web). Two strategies contributing to this posture will be exemplified, within the optics of Semantic-Logic Sociology: Experimental Books and Social Semantic-Logic Sites. They use the following instruments for producing/writing and receiving/reading social and semantic knowledge, some of these shown in the present paper: Visual Ontologies built from Social Hybridologies, GeoNeoLogic Methods (Multitouch Questionnaire, Trichotomies Game, etc..), Conceptual Abstracts, Present Books, Author-Actor Maps, GeoNeoLogic Novels, Visual Social Ontologies, Knowledge Interactive Windows, Visual Socio-Semantic Indexes, Visual Meta-Semantic Indexes. In short, Open Research and Open Digital Memories may constitute some of the fundamental pillars of emergent Research Society. This means a social paradigm where common citizens may become a sort of ‘lay researchers’ and, in the process, reformulate contemporary expert’s knowledge and power.Fundação para a Ciência e a Tecnologia (FCT

Strategic Argumentation is NP-Complete

In this paper we study the complexity of strategic argumentation for dialogue games. A dialogue game is a 2-player game where the parties play arguments. We show how to model dialogue games in a skeptical, non-monotonic formalism, and we show that the problem of deciding what move (set of rules) to play at each turn is an NP-complete problem

The Logic of Joint Ability in Two-Player Tacit Games

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality