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Search Results: 1 - 10 of 264 matches for " Dov Gabbay "
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The Attack as Intuitionistic Negation
Dov Gabbay,Michael Gabbay
Computer Science , 2015,
Abstract: We translate the argumentation networks ${\cal A}=(S, R)$ into a theory $D$ of intuitionistic logic, retaining $S$ as the domain and using intuitionistic negation to model the attack $R$ in ${\cal A}$: the attack $xRy$ is translated to $x\to\neg y$. The intuitionistic models of $D$ characterise the complete extensions of ${\cal A}$. The reduction of argumentation networks to intuitionistic logic yields, in addition to a representation theorem, some additional benefits: it allows us to give semantics to higher level attacks, where an attack "$xRy$" can itself attack another attack "$uRv$"; one can make higher level meta-statements $W$ on $(S, R)$ and such meta-statements can attack and be attacked in the domain.
The Attack as Strong Negation, Part I
Dov Gabbay,Michael Gabbay
Computer Science , 2015,
Abstract: We add strong negation $N$ to classical logic and interpret the attack relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a corresponding object level (using $N$ only) classical theory for each argumentation network and show that the classical models of this theory correspond exactly to the complete extensions of the argumentation network. We show by example how this approach simplifies the study of abstract argumentation networks. We compare with other translations of abstract argumentation networks into logic, such as classical predicate logic or modal logics, or logic programming, and we also compare with Abstract Dialectical Frameworks.
Equilibria und weiteres Heiteres
Dov Gabbay,Karl Schlechta
Mathematics , 2009,
Abstract: We investigate several technical and conceptual questions.
Semantic interpolation
Dov Gabbay,Karl Schlechta
Mathematics , 2009,
Abstract: We treat interpolation for various logics.
Size and Logic
Dov Gabbay,Karl Schlechta
Mathematics , 2009,
Abstract: We show how to develop a multitude of rules of nonmonotonic logic from very simple and natural notions of size, using them as building blocks.
A semantics for obligations
Dov Gabbay,Karl Schlechta
Mathematics , 2008,
Abstract: We analyze a number of properties obligations have or should have.
Logical tools for handling change in agent-based systems
Dov Gabbay,Karl Schlechta
Mathematics , 2008,
Abstract: We give a unified approach to various results and problems of nonclassical logics
Defeasible inheritance systems and reactive diagrams
Dov Gabbay,Karl Schlechta
Mathematics , 2008,
Abstract: We give an analysis of defeasible inheritance diagrams, also from the perspective of reactive diagrams.
Independence - revision and defaults
Dov Gabbay,Karl Schlechta
Mathematics , 2009,
Abstract: We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.
A theory of hierarchical consequence and conditionals
Dov Gabbay,Karl Schlechta
Mathematics , 2008,
Abstract: We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
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