636 research outputs found
Ecumenical modal logic
The discussion about how to put together Gentzen's systems for classical and
intuitionistic logic in a single unified system is back in fashion. Indeed,
recently Prawitz and others have been discussing the so called Ecumenical
Systems, where connectives from these logics can co-exist in peace. In Prawitz'
system, the classical logician and the intuitionistic logician would share the
universal quantifier, conjunction, negation, and the constant for the absurd,
but they would each have their own existential quantifier, disjunction, and
implication, with different meanings. Prawitz' main idea is that these
different meanings are given by a semantical framework that can be accepted by
both parties. In a recent work, Ecumenical sequent calculi and a nested system
were presented, and some very interesting proof theoretical properties of the
systems were established. In this work we extend Prawitz' Ecumenical idea to
alethic K-modalities
General-elimination stability
General-elimination harmony articulates Gentzen's idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies' test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett's notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable.Publisher PDFPeer reviewe
On the Proof Theory of Regular Fixed Points
International audienceWe consider encoding finite automata as least fixed points in a proof theoretical framework equipped with a general induction scheme, and study automata inclusion in that setting. We provide a coinductive characterization of inclusion that yields a natural bridge to proof-theory. This leads us to generalize these observations to regular formulas, obtaining new insights about inductive theorem proving and cyclic proofs in particular
Meaning and Dialogue Coherence: A Proof-theoretic Investigation
This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between agents and their environment. The order of explanation is opposite in direction to that adopted in game-theoretic semantics, where sentence semantics (or a notion of valid inference) is derived from winning dialogue strategies. That approach and the current one may, however, be reconcilable, since we focus on cooperative dialogue, whereas the game-theoretic tradition concentrates on adversarial dialogue
Models of HoTT and the Constructive View of Theories
Homotopy Type theory and its Model theory provide a novel formal semantic framework for representing scientific theories. This framework supports a constructive view of theories according to which a theory is essentially characterised by its methods.
The constructive view of theories was earlier defended by Ernest Nagel and a number of other philosophers of the past but available logical means did not allow these people to build formal representational frameworks that implement this view
Measurement of the Z/gamma* + b-jet cross section in pp collisions at 7 TeV
The production of b jets in association with a Z/gamma* boson is studied
using proton-proton collisions delivered by the LHC at a centre-of-mass energy
of 7 TeV and recorded by the CMS detector. The inclusive cross section for
Z/gamma* + b-jet production is measured in a sample corresponding to an
integrated luminosity of 2.2 inverse femtobarns. The Z/gamma* + b-jet cross
section with Z/gamma* to ll (where ll = ee or mu mu) for events with the
invariant mass 60 < M(ll) < 120 GeV, at least one b jet at the hadron level
with pT > 25 GeV and abs(eta) < 2.1, and a separation between the leptons and
the jets of Delta R > 0.5 is found to be 5.84 +/- 0.08 (stat.) +/- 0.72 (syst.)
+(0.25)/-(0.55) (theory) pb. The kinematic properties of the events are also
studied and found to be in agreement with the predictions made by the MadGraph
event generator with the parton shower and the hadronisation performed by
PYTHIA.Comment: Submitted to the Journal of High Energy Physic
- …