A logical basis for constructive systems

The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see http://www.cis.upenn.edu/~giorgi/cl.html). This article elaborates some basic complexity theory for the CoL framework. Then it proves soundness and completeness for the deductive system CL12 with respect to the semantics of CoL, including the version of the latter based on polynomial time computability instead of computability-in-principle. CL12 is a sequent calculus system, where the meaning of a sequent intuitively can be characterized as "the succedent is algorithmically reducible to the antecedent", and where formulas are built from predicate letters, function letters, variables, constants, identity, negation, parallel and choice connectives, and blind and choice quantifiers. A case is made that CL12 is an adequate logical basis for constructive applied theories, including complexity-oriented ones

Inattentive Consumers in Markets for Services

In an experiment on markets for services, we find that consumers are likely to stick to default tariffs and achieve suboptimal outcomes. We find that inattention to the task of choosing a better tariff is likely to be a substantial problem in addition to any task and tariff complexity effect. The institutional setup on which we primarily model our experiment is the UK electricity and gas markets, and our conclusion is that the new measures by the UK regulator Ofgem to improve consumer outcomes are likely to be of limited impact

A Complexity-Brightness Correlation in Gamma Ray Bursts

We observe strong correlations between the temporal properties of gamma ray bursts (GRBs) and their apparent peak brightness. The strongest effect (with a significance level of 10^{-6}) is the difference between the brightness distributions of simple bursts (dominated by a single smooth pulse) and complex bursts (consisting of overlapping pulses). The latter has a break at a peak flux of 1.5 ph/cm^2/s, while the distribution of simple bursts is smooth down to the BATSE threshold. We also observe brightness dependent variations in the shape of the average peak aligned time profile (ATP) of GRBs. The decaying slope of the ATP shows time dilation when comparing bright and dim bursts while the rising slope hardly changes. Both slopes of the ATP are deformed for weak bursts as compared to strong bursts. The interpretation of these effects is simple: a complex burst where a number of independent pulses overlap in time appears intrinsically stronger than a simple burst. Then the BATSE sample of complex bursts covers larger redshifts where some cosmological factor causes the break in the peak brightness distribution. This break could correspond to the peak in the star formation rate that was recently shown to occur at a redshift of z~1.5.Comment: 13 pages; 11 figures; replaced with the published versio

Emerging Consciousness as a Result of Complex-Dynamical Interaction Process

A quite general interaction process within a multi-component system is analysed by the extended effective potential method, liberated from usual limitations of perturbation theory or integrable model. The obtained causally complete solution of the many-body problem reveals the phenomenon of dynamic multivaluedness, or redundance, of emerging, incompatible system realisations and dynamic entanglement of system components within each realisation. The ensuing concept of dynamic complexity (and related intrinsic chaoticity) is absolutely universal and can be applied to the problem of consciousness that emerges now as a high enough, properly specified level of unreduced complexity of a suitable interaction process. This complexity level can be identified with the appearance of bound, permanently localised states in the multivalued brain dynamics from strongly chaotic states of unconscious intelligence, by analogy with classical behaviour emergence from quantum states at much lower levels of world dynamics. We show that the main properties of this dynamically emerging consciousness (and intelligence, at the preceding complexity level) correspond to empirically derived properties of natural versions and obtain causally substantiated conclusions about their artificial realisation, including the fundamentally justified paradigm of genuine machine consciousness. This rigorously defined machine consciousness is different from both natural consciousness and any mechanistic, dynamically single-valued imitation of the latter. We use then the same, truly universal concept of complexity to derive equally rigorous conclusions about mental and social implications of the machine consciousness paradigm, demonstrating its indispensable role in the next stage of civilisation development