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Monotonicity-based inference is a fundamental notion in the logical semantics of natural language, and also in logic in general. Start- ing in generalized quantifier theory, we distinguish three senses of the notion, study their relations, and use these to connect monotonicity to logics of model ...
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Given the preferences of several agents over a set of alternatives,there may be competing views on which of the alternatives would be the "best" compromise. We propose a formal model, grounded in social choice theory, for providing a justification for a given choice in the context of a given corp...
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By a combination of well-known results in judgment aggregation, it is essentially impossible to design an aggregation rule that simultaneously satisfies two crucial requirements: to always return an outcome that is logically consistent, and to be immune to strategic manipulation. To address this ...
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Suppose you want to design a voting rule that can be used to elect a committee or parliament by asking each voter to approve of a subset of the candidates standing. There are several properties you may want that rule to satisfy. First, voters should enjoy some form of proportional representation....
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We introduce a new approach for designing rules for participatory budgeting (PB), the problem of deciding on the use of public funds based directly on the views expressed by the citizens concerned. The core idea is to embed instances of the participatory budgeting problem into judgment aggregatio...
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Compositionality is a principle used in logic, philosophy, mathematics, linguistics, and computer science for assigning meanings to language ex- pressions in a systematic manner following syntactic construction, thereby allowing for a perspicuous algebraic view of the syntax-semantics inter- face...
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Suppose that a group of individuals are asked to aggregate their judgments on different—possibly logically interconnected—propositions in order to reach a collective decision. Quota rules are natural aggregation rules requiring that a proposition be collectively accepted if and only if the number...
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A particular family of imagination-based epistemologies of possibility promise to provide an account that overcomes problems raised by Kripkean a posteriori impossibilities. That is, they maintain that imagination plays a significant role in the epistemology of possibility. They claim that imagin...
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We investigate a recently-devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. We provide a necessary and sufficient condition f...
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We consider a randomised version of Kleene’s realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of randomly realisable statements is closed ...
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We articulate a relational understanding of modality, and show it at work in a survey of pre-order models, set-lifting, and modal languages.