Propositional Logics Complexity and the Sub-Formula Property

In 1979 Richard Statman proved, using proof-theory, that the purely implicational fragment of Intuitionistic Logic (M-imply) is PSPACE-complete. He showed a polynomially bounded translation from full Intuitionistic Propositional Logic into its implicational fragment. By the PSPACE-completeness of S4, proved by Ladner, and the Goedel translation from S4 into Intuitionistic Logic, the PSPACE- completeness of M-imply is drawn. The sub-formula principle for a deductive system for a logic L states that whenever F1,...,Fk proves A, there is a proof in which each formula occurrence is either a sub-formula of A or of some of Fi. In this work we extend Statman result and show that any propositional (possibly modal) structural logic satisfying a particular formulation of the sub-formula principle is in PSPACE. If the logic includes the minimal purely implicational logic then it is PSPACE-complete. As a consequence, EXPTIME-complete propositional logics, such as PDL and the common-knowledge epistemic logic with at least 2 agents satisfy this particular sub-formula principle, if and only if, PSPACE=EXPTIME. We also show how our technique can be used to prove that any finitely many-valued logic has the set of its tautologies in PSPACE.Comment: In Proceedings DCM 2014, arXiv:1504.0192

Achieving a designed customer experience across multiple delivery platforms: A telco perspective

'Customer experience' is a term that covers a wide range of activities that take place between suppliers and users of products and services. LaSalle and Britton define it as 'a holistic experience which involves a person - as opposed to a customer - as a whole at different levels and in every interaction between such person and a company' (2003). This research considers a key aspect of such an holistic experience: that which is embodied in the product or service under consideration. In the context of increasing mobile technology convergence, the paper considers new approaches that focus on developing the necessary underlying enablers and common interaction flows that are required to deliver a designed experience, taking into account the increasing number of mobile operating systems and service delivery platforms. Ultimately these models move towards allowing users to 'co-create their own unique experiences' (Pralahad and Ramswamy, 2004). The convergence between IT and telecommunications domains presents a unique challenge to product and service designers. Services are increasingly accessible via multiple delivery devices and delivery networks. This trend has been seen most recently in the advent of Internet based services being delivered via mobile phones where 'mobile service delivery and technologies have become the glue between previously secluded 'telecom' and "IT' domains' (Karrberg and Liebenau, 2006). At the same time network operators are trying to tighten their relationship with their customers by offering 'sticky' services aimed at raising the barriers to customer mobility. These two trends lead to a new design challenge: how to design a recognisably consistent and compelling product customer experience that applies over all delivery services, operating systems and networks. Solutions to this problem have to date been either technology led, focussing on integrated delivery platforms, or reliant on rule-based design. Crucial to this analysis is the 'role Please use this identifier to cite or link to this item

Bound states for Overlap and Fixed Point Actions close to the chiral limit

We study the overlap and the fixed point Dirac operators for massive fermions in the two-flavor lattice Schwinger model. The masses of the triplet (pion) and singlet (eta) bound states are determined down to small fermion masses and the mass dependence is compared with various continuum model approximations. Near the chiral limit, at very small fermion masses the fixed point operator has stability problems, which in this study are dominated by finite size effects,Comment: 13 pages, 2 figure

Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator

AMS classifications: 62G20, 62G32;asymptotic normality;confidence intervals;Edgeworth expansions;extreme value index;Hill estimator;regular variation;tail index

Edgeworth Expansions for the Distribution Function of the Hill Estimator

We establish Edgeworth expansions for the distribution function of the centered and normalized Hill estimator for the positive extreme value index.estimation;variation;statistical distribution

Proof-graphs for Minimal Implicational Logic

It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study how to reduce the weight of propositional deductions. We present the formalism of proof-graphs for purely implicational logic, which are graphs of a specific shape that are intended to capture the logical structure of a deduction. The advantage of this formalism is that formulas can be shared in the reduced proof. In the present paper we give a precise definition of proof-graphs for the minimal implicational logic, together with a normalization procedure for these proof-graphs. In contrast to standard tree-like formalisms, our normalization does not increase the number of nodes, when applied to the corresponding minimal proof-graph representations.Comment: In Proceedings DCM 2013, arXiv:1403.768