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In this paper we introduce a game semantics for System P, one of the most studied axiomatic systems for non-monotonic reasoning, conditional logic and belief revision. We prove soundness and completeness of the game semantics with respect to the rules of System P, and show that an inference is va...
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We develop the theory of stable modal logics, a class of modal logics introduced by Bezhanishvili, Bezhanishvili & Iemhoff (to appear). We give several new characterizations of stable modal logics, and show that there are continuum many such. Since some basic modal systems such as K4 and S4 are n...
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A system WF of subintuitionistic logic is introduced, weaker than Corsi's basic subintuitionistic system F. A derivation system with and without hypotheses is given in line with the authors' derivation system for F. A neighborhood semantics is introduced with a somewhat more complex definition th...
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The subintuitionistic logics introduced by Corsi and Restall are developed in a uniform manner. Proof systems are given for derivations without and with assumptions. The results are applied to give conservation theorems for intuitionistic logic IPC over Corsi's system F. For Visser's basic logic...
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Different agents may have different points of view. This can be modelled using different abstract argumentation frameworks, each consisting of a set of arguments and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a prof...
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We introduce the concept of group manipulation into the study of judgment aggregation and investigate the circumstances under which an aggregation rule may be subject to strategic misrepresentation of judgments by a group of agents. Our focus is on neutral aggregation rules, which treat all propo...
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When the members of a group have to make a decision, they can use a voting rule to aggregate their preferences. But which rule to use is a difficult question. Different rules have different properties, and social choice theorists have found arguments for and against most of them. These arguments ...
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A number of seminal results in the field of social choice theory demonstrate the difficulties of aggregating the preferences of several individual agents for the purpose of making a decision together. We show how to formalise three of the most important impossibility results of this kind---Arrow’...
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We review several different languages for collective decision making problems, in which agents express their judgments, opinions, or beliefs over elements of a logically structured domain. Several such languages have been proposed in the literature to compactly represent the questions on which th...
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Krull dimension measures the depth of the spectrum Spec(R) of a commutative ring R. Since Spec(R) is a spectral space, Krull dimension can be defined for spectral spaces. Utilizing Stone duality, it can also be defined for distributive lattices. For an arbitrary topological space, the notion of ...
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We study the n-universal model of the positive fragment of the intuitionistic propositional calculus IPC. We denote it by U*(n) and show that it is isomorphic to a generated submodel of the n-universal model of IPC, which is denoted by U(n). We show that this close resemblance makes U*(n) mirror ...