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We introduce a new topological semantics for evidence, evidence based belief, knowledge and learning. This setting generalizes (and in a sense improves on) the evidence models for belief due to van Benthem and Pacuit, as well as our own previous work on (a topological semantics for) Stalnaker's d...
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Minimal Logic, i.e. intuitionistic logic without the ex falso principle, is investigated in its original form with a negation symbol instead of a symbol denoting the contradiction. A Kripke semantics is developed for minimal logic and its sublogics with a still weaker negation by introducing a fu...
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Classical results in social choice theory on the susceptibility of voting rules to strategic manipulation make the assumption that the manipulator has complete information regarding the preferences of the other voters. In reality, however, voters only have incomplete information, which limits the...
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We introduce a model of preference diffusion in which agents in a social network update their preferences based on those of their influencers in the network, and we study the dynamics of this model. Preferences are modelled as ordinal rankings over a finite set of alternatives. At each time step,...
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Aldo Antonelli has proposed a new semantics for first-order predicate
logic that treats quantifiers using non-standard power sets. In this
note, we analyze and clarify this decidable semantics, explore the
resulting weak logical systems in terms of their semantics and proof
theory, and sharpen up...
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Going beyond the traditional focus on consequence and inference, logic can be broadened to an exact theory of general information-driven agency drawing on many sources, without giving up on its well-established mathematical modus operandi. We show how this broader agenda involves the design of ...
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Sabotage modal logic was proposed in 2003 as a format for analyzing games that modify the graphs they are played on. We investigate some model-theoretic and proof-theoretic aspects of sabotage modal logic, which has largely come to be viewed as an early dynamic logic of graph change. Our first co...
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In this paper we develop a bimodal perspective on possibility semantics, a framework allowing partiality of states that provides an alternative modeling for classical propositional and modal logics. In particular, we define a full and faithful translation of the basic modal logic K over possibili...
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‘Possibility semantics’ for classical logics is on the rise these days, and it throws interesting new light on the borderline between classical and intuitionistic logic.
This note is about a source from 1981 that is attracting some attention, a handwritten Tech Report from the Gronin...
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We consider the theory IΣμ, where μ is the least x such that IΣx together with all true Π1-sentences is inconsistent. We show that the provability logic of IΣμ coincides with that of PA, i.e. the Gödel–Löb provability logic GL. While arithmetical completeness of GL with respect to PA is establish...
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This paper develops the philosophy and technology needed for adding a supremum operator to the interpretability logic ILM of Peano Arithmetic (PA). It is well- known that any theories extending PA have a supremum in the interpretability ordering. While provable in PA, this fact is not reflected i...