3,638 research outputs found
Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)
We propose a monotonic logic of internalised non-monotonic or instant
interactive proofs (LiiP) and reconstruct an existing monotonic logic of
internalised monotonic or persistent interactive proofs (LiP) as a minimal
conservative extension of LiiP. Instant interactive proofs effect a fragile
epistemic impact in their intended communities of peer reviewers that consists
in the impermanent induction of the knowledge of their proof goal by means of
the knowledge of the proof with the interpreting reviewer: If my peer reviewer
knew my proof then she would at least then (in that instant) know that its
proof goal is true. Their impact is fragile and their induction of knowledge
impermanent in the sense of being the case possibly only at the instant of
learning the proof. This accounts for the important possibility of
internalising proofs of statements whose truth value can vary, which, as
opposed to invariant statements, cannot have persistent proofs. So instant
interactive proofs effect a temporary transfer of certain propositional
knowledge (knowable ephemeral facts) via the transmission of certain individual
knowledge (knowable non-monotonic proofs) in distributed systems of multiple
interacting agents.Comment: continuation of arXiv:1201.3667 ; published extended abstract:
DOI:10.1007/978-3-642-36039-8_16 ; related to arXiv:1208.591
A Galois-Connection between Cattell's and Szondi's Personality Profiles
We propose a computable Galois-connection between, on the one hand, Cattell's
16-Personality-Factor (16PF) Profiles, one of the most comprehensive and
widely-used personality measures for non-psychiatric populations and their
containing PsychEval Personality Profiles (PPPs) for psychiatric populations,
and, on the other hand, Szondi's personality profiles (SPPs), a less well-known
but, as we show, finer personality measure for psychiatric as well as
non-psychiatric populations (conceived as a unification of the depth psychology
of S. Freud, C.G. Jung, and A. Adler). The practical significance of our result
is that our Galois-connection provides a pair of computable, interpreting
translations between the two personality spaces of PPPs (containing the 16PFs)
and SPPs: one concrete from PPP-space to SPP-space (because SPPs are finer than
PPPs) and one abstract from SPP-space to PPP-space (because PPPs are coarser
than SPPs). Thus Cattell's and Szondi's personality-test results are mutually
interpretable and inter-translatable, even automatically by computers.Comment: closely related to arXiv:1403.2000 as explained in the first
paragrap
A Galois-Connection between Myers-Briggs' Type Indicators and Szondi's Personality Profiles
We propose a computable Galois-connection between Myers-Briggs' Type
Indicators (MBTIs), the most widely-used personality measure for
non-psychiatric populations (based on C.G. Jung's personality types), and
Szondi's personality profiles (SPPs), a less well-known but, as we show, finer
personality measure for psychiatric as well as non-psychiatric populations
(conceived as a unification of the depth psychology of S. Freud, C.G. Jung, and
A. Adler). The practical significance of our result is that our
Galois-connection provides a pair of computable, interpreting translations
between the two personality spaces of MBTIs and SPPs: one concrete from
MBTI-space to SPP-space (because SPPs are finer) and one abstract from
SPP-space to MBTI-space (because MBTIs are coarser). Thus Myers-Briggs' and
Szondi's personality-test results are mutually interpretable and
inter-translatable, even automatically by computers
Computer-Aided Discovery and Categorisation of Personality Axioms
We propose a computer-algebraic, order-theoretic framework based on
intuitionistic logic for the computer-aided discovery of personality axioms
from personality-test data and their mathematical categorisation into formal
personality theories in the spirit of F.~Klein's Erlanger Programm for
geometrical theories. As a result, formal personality theories can be
automatically generated, diagrammatically visualised, and mathematically
characterised in terms of categories of invariant-preserving transformations in
the sense of Klein and category theory. Our personality theories and categories
are induced by implicational invariants that are ground instances of
intuitionistic implication, which we postulate as axioms. In our mindset, the
essence of personality, and thus mental health and illness, is its invariance.
The truth of these axioms is algorithmically extracted from histories of
partially-ordered, symbolic data of observed behaviour. The personality-test
data and the personality theories are related by a Galois-connection in our
framework. As data format, we adopt the format of the symbolic values generated
by the Szondi-test, a personality test based on L.~Szondi's unifying,
depth-psychological theory of fate analysis.Comment: related to arXiv:1403.200
Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)
We produce a decidable super-intuitionistic normal modal logic of
internalised intuitionistic (and thus disjunctive and monotonic) interactive
proofs (LIiP) from an existing classical counterpart of classical monotonic
non-disjunctive interactive proofs (LiP). Intuitionistic interactive proofs
effect a durable epistemic impact in the possibly adversarial communication
medium CM (which is imagined as a distinguished agent), and only in that, that
consists in the permanent induction of the perfect and thus disjunctive
knowledge of their proof goal by means of CM's knowledge of the proof: If CM
knew my proof then CM would persistently and also disjunctively know that my
proof goal is true. So intuitionistic interactive proofs effect a lasting
transfer of disjunctive propositional knowledge (disjunctively knowable facts)
in the communication medium of multi-agent distributed systems via the
transmission of certain individual knowledge (knowable intuitionistic proofs).
Our (necessarily) CM-centred notion of proof is also a disjunctive explicit
refinement of KD45-belief, and yields also such a refinement of standard
S5-knowledge. Monotonicity but not communality is a commonality of LiP, LIiP,
and their internalised notions of proof. As a side-effect, we offer a short
internalised proof of the Disjunction Property of Intuitionistic Logic
(originally proved by Goedel).Comment: continuation of arXiv:1201.3667; extended start of Section 1 and 2.1;
extended paragraph after Fact 1; dropped the N-rule as primitive and proved
it derivable; other, non-intuitionistic family members: arXiv:1208.1842,
arXiv:1208.591
Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)
We propose parametric constructive Kripke-semantics for multi-agent
KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions
of two basic functional building blocks, namely bias (or viewpoint) and
visibility, functioning also as the parameters of the doxastic and epistemic
accessibility relation. The doxastic accessibility relates two possible worlds
whenever the application of the composition of bias with visibility to the
first world is equal to the application of visibility to the second world. The
epistemic accessibility is the transitive closure of the union of our doxastic
accessibility and its converse. Therefrom, accessibility relations for common
and distributed belief and knowledge can be constructed in a standard way. As a
result, we obtain a general definition of knowledge in terms of belief that
enables us to view S5-knowledge as accurate (unbiased and thus true)
KD45-belief, negation-complete belief and knowledge as exact KD45-belief and
S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and
accurate) KD45-belief, and all this generically for arbitrary functions of bias
and visibility. Our results can be seen as a semantic complement to previous
foundational results by Halpern et al. about the (un)definability and
(non-)reducibility of knowledge in terms of and to belief, respectively
Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)
We produce a decidable classical normal modal logic of internalised
negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP)
from an existing logical counterpart of non-monotonic or instant interactive
proofs (LiiP). LDiiP internalises agent-centric proof theories that are
negation-complete (maximal) and consistent (and hence strictly weaker than, for
example, Peano Arithmetic) and enjoy the disjunction property (like
Intuitionistic Logic). In other words, internalised proof theories are
ultrafilters and all internalised proof goals are definite in the sense of
being either provable or disprovable to an agent by means of disjunctive
internalised proofs (thus also called epistemic deciders). Still, LDiiP itself
is classical (monotonic, non-constructive), negation-incomplete, and does not
have the disjunction property. The price to pay for the negation completeness
of our interactive proofs is their non-monotonicity and non-communality (for
singleton agent communities only). As a normal modal logic, LDiiP enjoys a
standard Kripke-semantics, which we justify by invoking the Axiom of Choice on
LiiP's and then construct in terms of a concrete oracle-computable function.
LDiiP's agent-centric internalised notion of proof can also be viewed as a
negation-complete disjunctive explicit refinement of standard KD45-belief, and
yields a disjunctive but negation-incomplete explicit refinement of
S4-provability.Comment: Expanded Introduction. Added Footnote 4. Corrected Corollary 3 and 4.
Continuation of arXiv:1208.184
Asymptotic cones of finitely presented groups
Let G be a connected semisimple Lie group with at least one absolutely simple
factor S such that R-rank(S) is at least 2, and let be a uniform
lattice in G.
(a) If holds, then has a unique asymptotic cone up to
homeomorphism.
(b) If fails, then has asymptotic cones up to
homeomorphism.Comment: To appear in Advances in Mathematic
Pulsar Spin--Velocity Alignment: Further Results and Discussion
The reported alignment between the projected spin-axes and proper motion
directions of pulsars is revisited in the light of new data from Jodrell Bank
and Effelsberg. The present investigation uses 54 pulsars, the largest to date
sample of pulsars with proper-motion and absolute polarisation, to study this
effect. Our study has found strong evidence for pulsar spin-velocity alignment,
excluding that those two vectors are completely uncorrelated, with >99%
confidence. Although we cannot exclude the possibility of orthogonal
spin-velocity configurations, comparison of the data with simulations shows
that the scenario of aligned vectors is more likely than that of the orthogonal
case. Moreover, we have determined the spread of velocities that a spin-aligned
and spin-orthogonal distribution of kicks must have to produce the observed
distribution of spin-velocity angle offsets. If the observed distribution of
spin-velocity offset angles is the result of spin-aligned kicks, then we find
that the distribution of kick-velocity directions must be broad with
{\sigma}_v~30\degree if the orthogonal-kick scenario is assumed, then the
velocity distribution is much narrower with {\sigma}_v<10\degree. Finally, in
contrast to previous studies, we have performed robustness tests on our data,
in order to determine whether our conclusions are the result of a statistical
and/or systematic bias. The conclusion of a correlation between the spin and
velocity vectors is independent of a bias introduced by subsets in the total
sample. Moreover, we estimate that the observed alignment is robust to within
10% systematic uncertainties on the determination of the spin-axis direction
from polarisation data.Comment: 20 pages, 7 figures, 1 Table, accepted in MNRA
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