62 research outputs found
Monotonic Distributive Semilattices
In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {â, â§, â€}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de MatemĂĄtica; ArgentinaFil: MenchĂłn, MarĂa Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de MatemĂĄtica; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentin
Countermodel Construction via Optimal Hypersequent Calculi for Non-normal Modal Logics
International audienceWe develop semantically-oriented calculi for the cube of non-normal modal logics and some deontic extensions. The calculi manipulate hypersequents and have a simple semantic interpretation. Their main feature is that they allow for direct countermodel extraction. Moreover they provide an optimal decision procedure for the respective logics. They also enjoy standard proof-theoretical properties, such as a syntactical proof of cut-admissibility
Weakly Aggregative Modal Logic: Characterization and Interpolation
Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic
logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation
Research in progress: report on the ICAIL 2017 doctoral consortium
This paper arose out of the 2017 international conference on AI and law doctoral consortium. There were five students who presented their Ph.D. work, and each of them has contributed a section to this paper. The paper offers a view of what topics are currently engaging students, and shows the diversity of their interests and influences
Defining a General Structure of Four Inferential Processes by Means of Four Pairs of Choices Concerning Two Basic Dichotomies
In previous papers I have characterized four ways of reasoning in Peirceâs philosophy, and four ways of
reasoning in Computability Theory. I have established their correspondence on the basis of the four pairs
of choices regarding two dichotomies, respectively the dichotomy between two kinds of Mathematics and
the dichotomy between two kinds of Logic. In the present paper I introduce four principles of reasoning in
theoretical Physics and I interpret also them by means of the four pairs of choices regarding the above two
dichotomies. I show that there exists a meaningful correspondence among the previous three fourfold sets
of elements. This convergence of the characteristic ways of reasoning within three very different fields of
research - Peirceâs philosophy, Computability theory and physical theories - suggests that there exists a
general-purpose structure of four ways of reasoning. This structure is recognized as applied by Mendeleev
when he built his periodic table. Moreover, it is shown that a chemist-, applies all the above ways of
reasoning at the same time. Peirceâs professional practice as a chemist applying at the same time this
variety of reasoning explains his stubborn research into the variety of the possible inferences
Norms in Action: A Logical Perspective
The introduction to this chapter has been written by Emiliano Lorini and Giovanni SartorInternational audienceA theory of action is fundamental for legal theory, as the law is meant to direct behaviour: it influences the behaviour of agents who can understand the lawâs prescriptions and act accordingly. A connection between law and action is assumed by the most diverse approaches to the law; when no reference is made to this connection it is since it appears to be an obvious truism. Let us list just a few examples where this connection appears most clearly
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