472 research outputs found
On Counterfactuals and Contextuality
Counterfactual reasoning and contextuality is defined and critically
evaluated with regard to its nonempirical content. To this end, a uniqueness
property of states, explosion views and link observables are introduced. If
only a single context associated with a particular maximum set of observables
can be operationalized, then a context translation principle resolves
measurements of different contexts.Comment: 10 pages, presented at Foundations of Probability and Physics-3,
Vaexjoe University, Sweden, June 7-12, 200
Finite automata models of quantized systems: conceptual status and outlook
Since Edward Moore, finite automata theory has been inspired by physics, in
particular by quantum complementarity. We review automaton complementarity,
reversible automata and the connections to generalized urn models. Recent
developments in quantum information theory may have appropriate formalizations
in the automaton context.Comment: 12 pages, prepared for the Sixth International Conference on
Developments in Language Theory, Kyoto, Japan, September 18-21, 200
A pre-semantics for counterfactual conditionals and similar logics
The elegant Stalnaker/Lewis semantics for counterfactual conditonals works
with distances between models. But human beings certainly have no tables of
models and distances in their head. We begin here an investigation using a more
realistic picture, based on findings in neuroscience. We call it a
pre-semantics, as its meaning is not a description of the world, but of the
brain, whose structure is (partly) determined by the world it reasons about. In
the final section, we reconsider the components, and postulate that there are
no atomic pictures, we can always look inside
Towards the Integration of an Intuitionistic First-Order Prover into Coq
An efficient intuitionistic first-order prover integrated into Coq is useful
to replay proofs found by external automated theorem provers. We propose a
two-phase approach: An intuitionistic prover generates a certificate based on
the matrix characterization of intuitionistic first-order logic; the
certificate is then translated into a sequent-style proof.Comment: In Proceedings HaTT 2016, arXiv:1606.0542
Extending Kolmogorov's axioms for a generalized probability theory on collections of contexts
Kolmogorov's axioms of probability theory are extended to conditional
probabilities among distinct (and sometimes intertwining) contexts. Formally,
this amounts to row stochastic matrices whose entries characterize the
conditional probability to find some observable (postselection) in one context,
given an observable (preselection) in another context. As the respective
probabilities need not (but, depending on the physical/model realization, can)
be of the Born rule type, this generalizes approaches to quantum probabilities
by Auff\'eves and Grangier, which in turn are inspired by Gleason's theorem.Comment: 18 pages, 3 figures, greatly revise
Coherence in Modal Logic
A variety is said to be coherent if the finitely generated subalgebras of its
finitely presented members are also finitely presented. In a recent paper by
the authors it was shown that coherence forms a key ingredient of the uniform
deductive interpolation property for equational consequence in a variety, and a
general criterion was given for the failure of coherence (and hence uniform
deductive interpolation) in varieties of algebras with a term-definable
semilattice reduct. In this paper, a more general criterion is obtained and
used to prove the failure of coherence and uniform deductive interpolation for
a broad family of modal logics, including K, KT, K4, and S4
Reactive preferential structures and nonmonotonic consequence
We introduce information bearing systems (IBRS) as an abstraction of many
logical systems. We define a general semantics for IBRS, and show that IBRS
generalize in a natural way preferential semantics and solve open
representation problems
Disagreement about logic
Under embargo until: 2021-02-08What do we disagree about when we disagree about logic? On the face of it, classical and nonclassical logicians disagree about the laws of logic and the nature of logical properties. Yet, sometimes the parties are accused of talking past each other. The worry is that if the parties to the dispute do not mean the same thing with ‘if’, ‘or’, and ‘not’, they fail to have genuine disagreement about the laws in question. After the work of Quine, this objection against genuine disagreement about logic has been called the meaning-variance thesis. We argue that the meaning-variance thesis can be endorsed without blocking genuine disagreement. In fact, even the type of revisionism and nonapriorism championed by Quine turns out to be compatible with meaning-variance.acceptedVersio
On the undefinability of Tsirelson's space and its descendants
We prove that Tsirelson's space cannot be defined explicitly from the
classical Banach sequence spaces. We also prove that any Banach space that is
explicitly definable from a class of spaces that contain or must
contain or as well
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