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In this brief note, I discuss some general backgrounds of the well-known Fixed-Point Theorem for Provability Logic, taking my cues from an elegant abstract argument by Dick de Jongh in the 1980s.
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Onmogelijkheden zijn even belangrijk als mogelijkheden in de wetenschap en maatschappij. Een column van 300 woorden over Gödel in de reeks "Kleine Ode aan een Groot Idee".
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We prove that there exist profinite Heyting algebras that are not isomorphic to the profinite completion of any Heyting algebra. This resolves an open problem from 2009. More generally, we characterize those varieties of Heyting algebras in which profinite algebras are isomorphic to profinite com...
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We develop a uniform coalgebraic approach to Thomason and
Jonsson-Tarski type dualities for various classes of neighborhood frames and neighborhood algebras. In the first part of the paper we construct an endofunctor on the category of complete and atomic Boolean algebras that is dual to the do...
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We study the topological mu-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over T0 and TD spaces. We also investigate relational
mu-calculus, providing general completeness results for all ...
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Reasoning with generalized quantifiers in natural language combines logical and arithmetical features, transcending divides between qualitative and quantitative. This practice blends with inference patterns in ‘grassroots mathematics’ such as pigeon-hole principles. Our topic is this cooperation ...
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We propose a logic of imagination, based on simulated belief revision, that intends
to uncover the logical patterns governing the development of imagination
in pretense. Our system complements the currently prominent logics of imagination in that ours in particular formalises (1) the algorithm ...
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We introduce a new hybrid modal logic HSML for reason- ing about sabotage-style graph games with edge deletions, and provide a complete Hilbert-style axiomatization. We extend the completeness anal- ysis to protocol models with restrictions on available edge deletions, and clarify the connections...
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Vector spaces show a number of general structures that invite analysis in modal logics.
As such, they provide an interesting counterpart to the much better-studied modal logics of topology. At the same time, vector spaces pose several challenges to this style of analysis of a mathematical practi...
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A bi-Heyting algebra validates the Go ̈del-Dummett axiom (p → q) ∨ (q → p) iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-Heyting algebras of this form are called bi-Go ̈del algebras and form a variety that algebraizes the extension bi-LC of bi...