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We study propositional logical systems arising from the lan- guage of Johansson’s minimal logic and obtained by weakening the re- quirements for the negation operator. Using duality and completeness we prove that there are uncountably many such logical systems. We also give model-theoretic and al...
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We study the differences between finite identifiability of re- cursive languages with positive and with complete data. In finite families the difference lies exactly in the fact that for positive identification the families need to be anti-chains, while in in the infinite case it is less sim- ple...
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Judgment aggregation is a general framework for collective decision making that can be used to model many different settings. Due to its general nature, the worst case complexity of essentially all relevant problems in this framework is very high. However, these intractability results are mainly ...
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Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational problems for these logics have been studied for their comput...
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The standard topological representation of a Boolean algebra via the
clopen sets of a Stone space requires a nonconstructive choice principle, equivalent
to the Boolean Prime Ideal Theorem. In this paper, we describe a choice-free topo-
logical representation of Boolean algebras. This represen...
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Abstract. Let κ be an uncountable regular cardinal with κ<κ = κ. We
consider two totally ordered fields κ-R and Rκ, due to Sikorski and the second author, respectively, that serve as the κ-analogues of the real line and consider generalisations of the Bolzano-Weierstraß theorem for them, showing...
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An algebra-valued model of set theory is called loyal to its algebra if the model and its algebra have the same propositional logic; it is called faithful if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorp...
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I introduce a model of judgment aggregation that allows for an explicit distinction between rationality and feasibility constraints. The former are assumed to be satisfied by the individual agents; the latter must be met by the collective decision returned by the aggregation rule in use. Using th...
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When confronted with the same abstract argumentation framework, specifying a set of arguments and an attack-relation between them, different agents may disagree on which arguments to accept, i.e., they may choose different extensions. In the context of designing systems to support collective argu...
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In this paper we design a new logical system to explicitly model the different deductive reasoning steps of a boundedly rational agent. We present an adequate system in line with experimental findings about an agent’s reasoning limitations and the cognitive effort that is involved. Inspired by Dy...
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What general conclusions can be inferred logically from just observing single instances? We discuss three precise senses in which this can happen. In the broadcast view, a single truth in one model transmits other truths to suitably related models in ever widening circles, on the model of preserv...