We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results).
arXiv:2608. 15147v1 Announce Type: new Abstract: Machine intelligence has conquered the symbolic world but stalled at the physical one.
arXiv:2606. 28841v1 Announce Type: cross Abstract: Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify.
arXiv:2606. 03655v1 Announce Type: new Abstract: Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al.
The paper introduces a semantic elevation operator that transforms static semantic questions about a program into dynamic questions about whether a property is preserved after the program rewrites itself. It proves that for intensional transformations the elevated property remains undecidable, showing that the class of non‑verifiable properties is closed under this operator and that repeated application climbs the arithmetical hierarchy to Υ02‑completeness. The work also demonstrates that no finite tower of verifiers can provide an unconditional certificate of preservation, and suggests a categorical perspective for future exploration.
arXiv:2608. 04457v1 Announce Type: cross Abstract: As "AI Scientists" emerge to drive research via the Model Context Protocol (MCP), systems relying on ephemeral scripts will fail.
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
arXiv:2607. 15629v1 Announce Type: cross Abstract: Topos causal models recast causal inference inside a topos: a causal world is a presheaf, an intervention is a characteristic map into the subobject classifier, and reasoning is carried out in the intuitionistic internal language.
arXiv:2609.36279v1 Announce Type: cross Abstract: The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's va...
arXiv:2608.29311v1 Announce Type: new Abstract: Classic Formal Concept Analysis (FCA) primarily focuses on the positive relationships between objects and attributes and does not have mechanisms for h...
The paper introduces Positive Topology, a framework built on a basic relation between points (or models) and observable properties. It identifies two complementary structures: universal refinement and cover, and positivity and witnessed existence, showing that each can reconstruct the underlying relation. The authors present both information‑theoretic and game‑theoretic interpretations, and discuss how resource constraints can be integrated, illustrating applications in medical diagnosis, legal reasoning, and AI.
arXiv:2609.06127v1 Announce Type: cross Abstract: Retrieval-augmented generation is usually formulated as a statistical information-retrieval problem. Graph-based variants add relational structure, b...