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Computing with Infinite Objects: the Gray Code Case [PDF]
Logical Methods in Computer Science, 2023 Infinite Gray code has been introduced by Tsuiki as a redundancy-free representation of the reals. In applications the signed digit representation is mostly used which has maximal redundancy.
Dieter Spreen, Ulrich Berger
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Axiomatization of betweenness in order-theoretic trees [PDF]
Logical Methods in Computer Science, 2021 The ternary betweenness relation of a tree, B(x,y,z) expresses that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes larger than any node is linearly ...
Bruno Courcelle
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Convexity via Weak Distributive Laws [PDF]
Logical Methods in Computer Science, 2022 We study the canonical weak distributive law $\delta$ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields.
Filippo Bonchi, Alessio Santamaria
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Overlap Algebras: a Constructive Look at Complete Boolean Algebras [PDF]
Logical Methods in Computer Science, 2020 The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set.
Francesco Ciraulo, Michele Contente
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Canonicity and homotopy canonicity for cubical type theory [PDF]
Logical Methods in Computer Science, 2022 Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices.
Thierry Coquand +2 more
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Reachability for infinite time Turing machines with long tapes [PDF]
Logical Methods in Computer Science, 2020 Infinite time Turing machine models with tape length $\alpha$, denoted $T_\alpha$, strengthen the machines of Hamkins and Kidder [HL00] with tape length $\omega$. A new phenomenon is that for some countable ordinals $\alpha$, some cells cannot be halting
Merlin Carl +2 more
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Dynamic Cantor Derivative Logic [PDF]
Logical Methods in Computer Science, 2023 Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as $d$-logics. Unlike logics based on the topological closure operator, $d$-logics have not previously been studied in the ...
David Fernández-Duque, Yoàv Montacute
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Universal Horn Sentences and the Joint Embedding Property [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The finite models of a universal sentence $\Phi$ in a finite relational signature are the age of a structure if and only if $\Phi$ has the joint embedding property. We prove that the computational problem whether a given universal sentence $\Phi$ has the
Manuel Bodirsky +2 more
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Approximation systems for functions in topological and in metric spaces [PDF]
Logical Methods in Computer Science, 2013 A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names.
Dimiter Skordev
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A Cubical Language for Bishop Sets [PDF]
Logical Methods in Computer Science, 2022 We present XTT, a version of Cartesian cubical type theory specialized for Bishop sets \`a la Coquand, in which every type enjoys a definitional version of the uniqueness of identity proofs.
Jonathan Sterling +2 more
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