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115 items with this tag.

Oct 30, 2026
THEORY-1239: No logistic system, one that separates propositions from general laws of inference, can carry commonsense knowledge, whose defaults later evidence displaces: attempts to repair its monotonicity will continue to fail
- logic
- cognition
Oct 29, 2026
QUESTION-332: Is the communicative object a presheaf over contexts?
- logic
- mathematics
Oct 29, 2026
THEORY-1142: A translation between two logics presented as institutions is correct, in the Satisfaction Condition's sense, when a translated sentence holds in a model exactly when the original holds in the model's translation; given the model translation this fixes the sentence translation up to semantic equivalence, and when every model of the target is reached it preserves and reflects entailment, so one logic's prover can decide the other's; but the condition alone admits collapsing translations and is relative to a model translation it does not supply
Oct 29, 2026
THEORY-1150: In any logical system presented as an institution, theories can be glued wherever their vocabularies can: if the category of signatures has colimits, so does the category of theories, the glued theory being the semantic closure of the union of the parts' translated sentences; and because constraints requiring free or initial interpretation also obey the Satisfaction Condition, theories carrying them glue the same way
- logic
- mathematics
Oct 27, 2026
CLAIM-457: That no single institution can bring about a remedy does not imply that no combination of them can: the institutions able together to realize a corrective outcome need include none able alone, so a true statement of unilateral inability is not a statement that the outcome is unattainable
Oct 27, 2026
CLAIM-479: In the record a typed relation is more constrained than either of its relata: a claim's content is open prose, while rests_on fixes the scheme at both ends, has supports written as its converse and says what retiring its target leaves, and none of that moves when either claim's content does; so a relation's rigidity is a fact about the grammar, not evidence that the dependency it records is sound
Oct 27, 2026
LIT-1633: Mr. Russell's "Causal Theory of Perception"
Oct 27, 2026
LIT-1643: Belief, awareness, and limited reasoning
- logic
- epistemology
Oct 27, 2026
LIT-1645: Logic: The Theory of Inquiry
Oct 27, 2026
LIT-1652: Counterexample-Guided Abstraction Refinement
- logic
- mathematics
Oct 27, 2026
LIT-1661: Institutions: abstract model theory for specification and programming
- logic
- mathematics
Oct 27, 2026
QUESTION-279: What would certify that no remedy is available to an institutional arrangement, rather than that its present procedures failed to find, authorize or carry one out before the deadline?
Oct 27, 2026
THEORY-1064: In counterexample-guided abstraction refinement, a spurious counterexample locates the distinction its abstraction lacked: walking it forward through the concrete system, the first abstract state where no concrete continuation exists merges the states the trace can reach with the states that have the transition onward, and splitting them removes the counterexample; for finite-state programs and ACTL* properties whose counterexamples are paths or loops, repeating check and split ends in a real counterexample or a proof
- logic
- mathematics
Oct 27, 2026
THEORY-1094: In counterexample-guided abstraction refinement the property and the concrete system are fixed inputs: the property's atomic formulas help build the first abstraction and no abstraction may merge states that disagree on them, every refinement only splits classes toward the concrete state space, and a real counterexample ends the procedure; so the loop revises which of the concrete system's distinctions the model draws, never the property or the space of possible answers
- logic
- mathematics
Oct 21, 2026
QUESTION-247: If the communicative object is a presheaf of propositions over a category of contexts, is the negation its topos logic gives an orthocomplement or a Heyting pseudo-complement, and what fixes it?
Oct 20, 2026
QUESTION-225: Are why-provenance and, for traceable queries, where-provenance preserved by Buneman, Khanna and Tan's rewrite system, and is traceability necessary for where-provenance to be preserved?
- databases
- logic
Oct 20, 2026
THEORY-807: The guppy-type overextension in Hampton's membership data arises because a combined concept is in part a new, emergent concept and not only a logical combination of its parts, so human concept combination runs in two superposed layers, one classical and logical and one quantum and conceptual
Oct 19, 2026
QUESTION-152: Does the impossibility of robustly rational proposition-wise aggregation extend from categorical judgments to corporate attitudes in general: degrees of belief, desires, intentions or emotions?
Oct 19, 2026
QUESTION-156: Which published models of concept combination reproduce overextension by dropping conjunction-as-meet, and which by dropping an order-preserving membership weight?
Oct 19, 2026
QUESTION-188: Is delete-and-rederive correct for recursive Datalog views with stratified negation and aggregation, and how large is its overestimate of deletions against the deletions actually needed?
- databases
- logic
Oct 19, 2026
THEORY-725: On the court agenda {P, Q, R, R iff (P and Q)} under universal domain, proposition-wise majority voting is not robustly rational, while the premise-based procedure is, and it makes the group's judgments a function of the members' whole judgment sets that the members' judgments on the conclusion neither fix nor need to enter
Oct 18, 2026
LIT-1213: Knowledge and common knowledge in a distributed environment
Oct 16, 2026
THEORY-462: If commonsense knowledge includes defaults that later evidence displaces, a monotonic logic, in which an added axiom can never remove a theorem, cannot represent that displacement as it stands; Minsky's further claim, that no logistic system, one that separates propositions from general laws of inference, can carry commonsense knowledge even once repaired, is asserted, not shown
- logic
- cognition
Oct 16, 2026
THEORY-493: From core mereology, classical extensional mereology (GEM) is reached by exactly three pairings of a decomposition principle with an unrestricted-sum principle: Supplementation with Sum2, Strong Supplementation with Sum3, and Complementation with Sum1; Supplementation with Sum3, the pairing given by Simons (1987), does not yield it, because which definition of 'sum' is used decides which decomposition axiom is needed
Oct 16, 2026
THEORY-516: For any presheaf of propositions over a small category of contexts, a sieve-valued valuation satisfies the generalized functional-composition condition exactly when it is a subobject of that presheaf, and the construction runs unchanged in classical physics, where every microstate gives a global section yet truth values are still non-Boolean sieves; so the logic of the truth values is fixed by the base category, not by whether a presheaf has global sections
Oct 16, 2026
THEORY-535: Quantum systems read as bundles of property-instances with no principle of individuality can have their kinds and their number stated in quasi-set theory, so that N indistinguishable particles get a definite quasi-cardinal without labels; the construction covers kinds and counting only, not states, actualization or dynamics
Oct 16, 2026
THEORY-544: In homotopy type theory extended with a strict directed interval and a layer of shapes, one contractibility condition, the Segal condition, gives a type identities, associativity and three-dimensional coherence, makes every function between Segal types a functor, and yields a dependent Yoneda lemma for covariant families; that such types are (∞,1)-categories rests on a semantics only sketched
- mathematics
- logic
Oct 16, 2026
THEORY-595: A filter over a set of worlds is a finitely consistent propositional theory and an ultrafilter a negation-complete one; read so, the ultrafilter extension theorem is Lindenbaum's lemma for propositions, and Łoś's theorem builds a model that makes true exactly what an ultrafilter says, which proves first-order compactness without proof theory, given the axiom of choice
- logic
- mathematics
Oct 16, 2026
THEORY-619: Over the poset of commutative von Neumann subalgebras, coarse-graining a projector to a smaller subalgebra is exactly the direct image of its clopen region of the Gelfand spectrum under restriction, so the coarse-graining presheaf is the presheaf of clopen spectral regions; and a quantum state's sieve-valued truth values are fixed by one coherent family of regions, its supports: a proposition is true at a subcontext exactly when the support there lies under the coarse-grained proposition
Oct 16, 2026
THEORY-642: Basic two-level type theory, an inner homotopy type theory with an outer level of strict equality, is conservative over homotopy type theory, so an inner type it proves inhabited is already inhabited in HoTT, but a fibrant-replacement type former would force uniqueness of identity proofs on the inner level
- mathematics
- logic
Oct 16, 2026
THEORY-647: If outright belief is credence ultraclose to 1 relative to a context level, conjunction holds for any standard ('few') number of believed propositions and fails for an ultralarge number, which dissolves the Lottery Paradox as an accumulation of negligible rounding errors
- epistemology
- logic
Oct 16, 2026
THEORY-649: When agents holding uniformly random consistent theories over two or three atomic sentences each average their theories once, bit by bit, with all peers within a Hamming bound of confidence, an individual agent ends up with the inconsistent theory at most 1.81% of the time, but the chance that some agent in the group does reaches 6.4% for two sentences and 16.9% for three
Oct 16, 2026
THEORY-665: Asserting is undertaking a commitment that entitles others to reassert it and carries a responsibility to show entitlement if challenged; every interlocutor keeps score of everyone's commitments and entitlements, so the score is doubly perspectival, and a speech act's significance is the change it makes to the scores, fixed by its content's inferential role
Oct 16, 2026
THEORY-698: Thresholding linear attribute probes on a language model's embeddings yields a complete concept lattice for any incidence whatever, so the lattice is guaranteed by construction; what the Lattice Representation Hypothesis measured is per-attribute agreement with GPT-4o annotations at F1 70–83, and no lattice law
Oct 15, 2026
CLAIM-306: Under a deadline, search can establish presence by finding one item but absence only by exhausting the collection, so "If I can't find it, it isn't there" acts on an unfinished search as negation as failure acts on a finished one: a default stronger than either the closed-world assumption or negation as failure, safe only when the arrangement makes the full search finish within the deadline
Oct 15, 2026
CLAIM-311: A search cut off before an exhaustive pass can establish absence when the arrangement certifies that the unsearched remainder cannot hold the item: a sorted table answers non-membership in a logarithmic number of probes, and the Threshold Algorithm stops early with its answer proved, so absence needs a certificate about the remainder, not exhaustion; similarity search in high dimension is where no such certificate exists
Oct 15, 2026
CLAIM-312: "If I can't find it, it isn't there" asserts operational unavailability, that the item will not be put to use before the deadline, not absence: a search that fails by the deadline establishes unavailability outright, and licenses absence only with a certificate that the unsearched remainder cannot hold the item, from exhaustion, from an invariant of the arrangement, or from a closed-world default
Oct 15, 2026
LIT-1050: On the logic of theory change: Partial meet contraction and revision functions
- logic
- epistemology
Oct 15, 2026
LIT-1072: Logic of Belief Revision
- logic
- epistemology
Oct 15, 2026
LIT-1087: Negation as Failure
- logic
Oct 15, 2026
LIT-1088: On Closed World Data Bases
- logic
Oct 15, 2026
LIT-1100: Answering Queries Using Views
- databases
- logic
Oct 15, 2026
LIT-1104: Why and Where: A Characterization of Data Provenance
- databases
- logic
Oct 15, 2026
LIT-1110: Provenance Semirings
Oct 15, 2026
LIT-1111: Optimal Implementation of Conjunctive Queries in Relational Data Bases
- databases
- logic
Oct 15, 2026
LIT-1114: Maintaining Views Incrementally
- databases
- logic
Oct 15, 2026
LIT-1116: Answering Queries Using Views: A Survey
- databases
- logic
Oct 15, 2026
THEORY-341: Inferring not-P from failure to prove P is a deduction only under two separate conditions: Clark shows that when every branch of the search for a proof of P ends in failure, not-P is a theorem of the completed database, and a search that does not finish licenses nothing; Reiter's closed-world assumption, adding the negation of every ground atom the database does not entail, keeps a consistent Horn database consistent and can make a disjunctive one inconsistent
- logic
- databases
Oct 15, 2026
THEORY-347: Belief bases with the same logical closure can revise to opposite conclusions on the same input, so a closed belief set does not fix its own revision; partial meet contraction of a base need not satisfy Recovery, and bases keep distinct inconsistent states apart, while a belief-set model reproduces the base difference only by attaching a different selection mechanism to the same set
- logic
- epistemology
Oct 15, 2026
THEORY-353: For a logically closed theory, the contractions satisfying the six basic AGM postulates are exactly the partial meet contractions, and those satisfying the two supplementary postulates as well are exactly the ones whose selection of remainders is generated by a transitive relation; the theory alone does not fix the contraction, and the results concern one change of one fixed theory
- logic
- epistemology
Oct 15, 2026
THEORY-362: For nonrecursive Datalog or SQL views with safe stratified negation and stratified aggregation, under set or duplicate semantics, storing with each derived tuple only the number of its derivations suffices to maintain the view under insertions and deletions of base tuples: signed counts propagated through delta rules stratum by stratum give each tuple's change as its new count minus its old, a tuple leaves when its count reaches zero, and a MIN or MAX group whose extreme is deleted is recomputed from the stored lower stratum
- databases
- logic
Oct 15, 2026
THEORY-367: For SPJU relational queries, which Buneman, Khanna and Tan's tree model encodes, the minimal witnesses of an output tuple, the inclusion-minimal sets of source facts from which the query still derives it, are the minimal sets matched by single derivations and so are the same for every equivalent query, while where-provenance, the source location a value was copied from, can differ between equivalent queries
- databases
- logic
Oct 15, 2026
THEORY-371: For conjunctive queries without equality or comparisons, two queries are equivalent exactly when homomorphisms run both ways between the queries read as small databases, every such query has a minimal equivalent query unique up to isomorphism obtained by deleting atoms, and evaluating one against a database is NP-complete when the query is part of the input
Oct 15, 2026
THEORY-373: For positive relational algebra on relations whose tuples are annotated from a commutative semiring, every query's annotated answer equals its answer over provenance polynomials N[X] in the input tuple ids, evaluated at the input annotations, so set, bag, c-table and event-table semantics all factor through the polynomials; revaluing inputs can remove output tuples but never add them, and nothing is shown for negation, difference or aggregation
Oct 15, 2026
THEORY-374: Given views with conjunctive definitions, deciding that they answer a conjunctive query exactly is NP-complete in the size of the query and definitions, while a maximally-contained rewriting can be built in time polynomial in that size without saying whether it is exact; and finding all certain answers from the stored contents is polynomial in their size under the open-world assumption when the views are conjunctive and the query conjunctive or datalog, but co-NP-hard in that size under the closed-world assumption even for conjunctive views and queries
- databases
- logic
Oct 15, 2026
THEORY-380: For datalog over a finite input instance annotated from a commutative ω-continuous semiring, with an answer's tag defined as the sum over its derivation trees of the product of its leaves' tags, the tags are the least fixed point of a finite polynomial system and factor through formal power series N∞⟦X⟧ in the input tuple ids; an answer tuple's series has an infinite coefficient exactly when one of its derivation trees contains a tuple lying on a cycle of unit rules
Oct 15, 2026
THEORY-387: For positive recursive Datalog views under set semantics, deleting every derived tuple that has any derivation through a deleted base fact, then restoring each deleted tuple that still has a derivation from what remains, then adding what insertions derive, leaves exactly the tuples derivable from the new base (E − Δ⁻) ∪ Δ⁺, with no derivation counts stored; the extension to stratified negation and aggregation is asserted, not shown, and the size of the overestimate is not measured
- databases
- logic
Oct 15, 2026
THEORY-389: For conjunctive queries and views without comparison predicates, a stored view can be used in an equivalent rewriting of a query exactly when the view's body maps homomorphically into the query's, a minimal rewriting needs no more literals than the query, and deciding whether a rewriting shorter than the query or one using only the views exists is NP-complete in the size of the query and view definitions; with comparisons in both, deciding whether any rewriting uses the views is Π2p-complete
- databases
- logic
Oct 14, 2026
THEORY-255: In Aerts's subspace model of Hampton's membership data, and in any lattice whose membership weight is order-preserving, whatever its negation, taking concept conjunction and disjunction as meet and join cannot produce overextension or underextension, so a model of the guppy-type deviations must take conjunction as some operation other than the meet or drop the monotone weight, while the Kolmogorov-type deviations can be had from the meet of a non-Boolean subspace lattice
Oct 13, 2026
LIT-1019: Information Flow: The Logic of Distributed Systems
- logic
- information-theory
Oct 12, 2026
LIT-934: Quantum structure in cognition
Oct 12, 2026
LIT-956: Back and forth between algebraic geometry, algebraic logic, sheaves and forcing
- logic
- mathematics
Oct 12, 2026
QUESTION-055: If communicative categories form a non-Boolean lattice, and the communicative object is a presheaf over contexts, over which base category is it one, and does some probe family split it into sectors that no probe connects?
Oct 09, 2026
LIT-794: Making It Explicit: Reasoning, Representing, and Discursive Commitment
Oct 09, 2026
LIT-818: Defaults in Update Semantics
Oct 09, 2026
LIT-838: The Semantics of Definite and Indefinite Noun Phrases
Oct 09, 2026
LIT-841: Semantic Unification: A Sheaf Theoretic Approach to Natural Language
Oct 09, 2026
LIT-843: Combining contextuality and causality: a game semantics approach
Oct 09, 2026
LIT-845: Closing Bell: Boxing black box simulations in the resource theory of contextuality
Oct 09, 2026
THEORY-162: What an utterance does to the context it is used in is part of its meaning, and its truth conditions do not fix it: sentences with the same truth conditions can differ in what they make available to later discourse, in whether they inform or only test, and in whether they describe a state of affairs or bring one about
Oct 04, 2026
THEORY-127: On the court agenda, and on any agenda in which every proposition reaches every other by conditional entailment and some minimally inconsistent triple stays consistent with two of its members negated, a group whose judgments are robustly rational under universal domain and respect unanimity cannot form its judgment on each proposition from its members' judgments on that proposition alone unless one member dictates; its judgments must supervene on the members' whole sets of judgments, and so can depart from what the members judge on the same proposition while being wholly fixed by them
Oct 01, 2026
LIT-378: 'What is a Thing?': Topos Theory in the Foundations of Physics
Oct 01, 2026
LIT-380: A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category
Oct 01, 2026
LIT-381: A Topos Perspective on the Kochen-Specker Theorem: II. Conceptual Aspects, and Classical Analogues
Oct 01, 2026
LIT-382: A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations
Oct 01, 2026
LIT-389: Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity
Oct 01, 2026
LIT-390: Topos Theory and Consistent Histories: The Internal Logic of the Set of All Consistent Sets
Oct 01, 2026
LIT-408: Jokes and the Logic of the Cognitive Unconscious
Oct 01, 2026
LIT-410: A Framework for Representing Knowledge
Oct 01, 2026
LIT-423: I Am a Strange Loop
Oct 01, 2026
LIT-437: Gödel, Escher, Bach: an Eternal Golden Braid
Sep 30, 2026
THEORY-020: Every Boolean algebra is the clopen algebra of its Stone space of prime ideals, and a finite one is the power set of its atoms, so a single Boolean context always has two-valued valuations and the Kochen–Specker obstruction lies in how contexts overlap
Sep 30, 2026
THEORY-024: Classical Boolean logic is restored when a presheaf of contextual data acquires a global section or is sheafified
Sep 30, 2026
THEORY-037: In the topos programme quantum propositions form a distributive Heyting algebra, not an orthocomplemented lattice, and its negation is a pseudo-complement under which excluded middle can fail
Sep 30, 2026
THEORY-041: Birkhoff and von Neumann proposed the modular law, not orthomodularity, and proved it fails for closed subspaces in infinite dimension; Husimi used the orthomodular identity only as an unnamed proof step
Sep 30, 2026
THEORY-042: Under a superselection rule a coherent superposition across sectors is operationally a mixture, because no observable connects the sectors; Wick, Wightman and Wigner proved such a rule for integer versus half-integer spin and only postulated it for charge
Sep 29, 2026
LIT-298: The problem of hidden variables in quantum mechanics
Sep 29, 2026
LIT-299: A topos foundation for theories of physics: III. The representation of physical quantities with arrows δ̆°(A): Σ̲ → ℝ̲≽
Sep 29, 2026
LIT-303: Types and Ontology
Sep 29, 2026
LIT-306: The logic of quantum mechanics
Sep 29, 2026
LIT-310: A topos foundation for theories of physics: IV. Categories of systems
Sep 29, 2026
LIT-318: The Concept of Mind
Sep 29, 2026
LIT-325: A topos perspective on the Kochen–Specker theorem: I. Quantum states as generalized valuations
Sep 29, 2026
LIT-335: A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory
Sep 29, 2026
LIT-337: Boolean Concept Logic
Sep 29, 2026
LIT-340: A theory of concepts and their combinations I: The structure of the sets of contexts and properties
Sep 29, 2026
LIT-343: A topos foundation for theories of physics: I. Formal languages for physics
Sep 29, 2026
LIT-344: Formal Concept Analysis: Mathematical Foundations
Sep 29, 2026
LIT-350: Categories and De Interpretatione (Clarendon Aristotle Series, trans. and notes J. L. Ackrill)
Sep 29, 2026
LIT-353: The Theory of Representations for Boolean Algebras
- mathematics
- logic
Sep 29, 2026
LIT-357: Studies on the Foundation of Quantum Mechanics. I
Sep 29, 2026
LIT-358: Applications of the theory of Boolean rings to general topology
- mathematics
- logic
Sep 27, 2026
LIT-262: The Geometry of Information Retrieval
Sep 27, 2026
LIT-267: The Lattice Representation Hypothesis of Large Language Models
Sep 27, 2026
LIT-272: Reasoning about Meaning in Natural Language with Compact Closed Categories and Frobenius Algebras
Sep 27, 2026
LIT-273: Mathematical Foundations for a Compositional Distributional Model of Meaning
Sep 27, 2026
LIT-276: Measurement as Sheafification: Context, Logic, and Truth after Quantum Mechanics
Sep 27, 2026
LIT-278: Contextuality, Cohomology and Paradox
Sep 27, 2026
LIT-281: Logical and Topological Contextuality in Quantum Mechanics and Beyond
Sep 26, 2026
LIT-095: Two-Level Type Theory and Applications
- mathematics
- logic
Sep 26, 2026
LIT-106: Brandom's Inferentialist Theory and the Meaning Entitlement Connection
Sep 26, 2026
LIT-107: Quasi-set theory: a formal approach to a quantum ontology of properties
Sep 26, 2026
LIT-145: Ultrafilters as Propositional Theories
- logic
- mathematics
Sep 25, 2026
LIT-032: A type theory for synthetic ∞-categories
- mathematics
- logic
Sep 25, 2026
LIT-054: A complete graphical calculus for Spekkens' toy bit theory

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