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Brouwer’s intuitionism is characterized by sequences not completely determined by a law: choice sequences. Initially Brouwer used only global properties of choice sequences, as in his reaching the continuum from the discrete. But in the late nineteen twenties he found a way to apply particular c...
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In 1938, Tarski proved that a formula is not intuitionistically valid
if, and only if, it has a counter-model in the Heyting algebra of open sets of
some topological space. In fact, Tarski showed that any Euclidean space R^n
with n > 1 suffices, as does e.g. the Cantor space. In particular, in...
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We set up a generic framework for proving completeness results for variants of the modal mu-calculus, using tools from coalgebraic modal logic. We illustrate the method by proving two new completeness results: for the graded mu-calculus (which is equivalent to monadic second-order logic on the cl...
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We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for c...
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We introduce a simple propositional calculus for compact Hausdorff spaces. Our approach is based on de Vries duality. The main new connective of our calculus is that of strict implication. We define the strict implication calculus SIC as our base calculus. We show that the corresponding variety S...
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This paper models collective decision-making scenarios by using a priority-based aggregation procedure, the so-called lexicographic method, in order to represent a form of reliability-based 'deliberation'. More precisely, it considers agents with a preference ordering over a set of objects and a ...
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In this paper we use infinitary Turing machines with tapes of length $\kappa$ and which run for time $\kappa$ as presented, e.g., by Koepke \& Seyfferth, to generalise the notion of type two computability to $\cantor$, where $\kappa$ is an uncountable cardinal with $\kappa^{<\kappa}=\kappa$. Then...
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We analyse the problem of finding an allocation of resources in a multiagent system that is as fair as possible in terms of minimising inequality between the utility levels enjoyed by the individual agents. We use the well-known Atkinson index to measure inequality and we focus on the distributed...
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It is well-known that non-standard models of Peano Arithmetic have order type N + Z·D where D is a dense linear order without first or last element. Not every order of the form N + Z·D is the order type of a model of Peano Arithmetic, though; in general, it is not known how to characterise those ...
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An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the second. When modelling a group of agents engaged in a debate, ...
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Different agents may have different points of view. Following a popular approach in the artificial intelligence literature, this can be modeled by means of different abstract argumentation frameworks, each consisting of a set of arguments the agent is contemplating and a binary attack-relation be...