One-dimensional fragment of first-order logic

We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified formula. The fragment is closed under Boolean operations, but additional restrictions (called uniformity conditions) apply to combinations of atomic formulae with two or more variables. We argue that the notions of one-dimensionality and uniformity together offer a novel perspective on the robust decidability of modal logics. We also establish that minor modifications to the restrictions of the syntax of the one-dimensional fragment lead to undecidable formalisms. Namely, the two-dimensional and non-uniform one-dimensional fragments are shown undecidable. Finally, we prove that with regard to expressivity, the one-dimensional fragment is incomparable with both the guarded negation fragment and two-variable logic with counting. Our proof of the decidability of the one-dimensional fragment is based on a technique involving a direct reduction to the monadic class of first-order logic. The novel technique is itself of an independent mathematical interest

Edge-promoting reconstruction of absorption and diffusivity in optical tomography

In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption and diffusivity. In this work, it is assumed that the imaged object is composed of an approximately homogeneous background with clearly distinguishable embedded inhomogeneities. An algorithm for finding the maximum a posteriori estimate for the absorption and diffusion coefficients is introduced assuming an edge-preferring prior and an additive Gaussian measurement noise model. The method is based on iteratively combining a lagged diffusivity step and a linearization of the measurement model of diffuse optical tomography with priorconditioned LSQR. The performance of the reconstruction technique is tested via three-dimensional numerical experiments with simulated measurement data.Comment: 18 pages, 6 figure

A Completeness Proof for A Regular Predicate Logic with Undefined Truth Value

We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of "is defined" is extended to terms and formulas via a straightforward recursive algorithm. The "is defined" formulas are constructed so that they themselves are always defined. The completeness proof relies on the Henkin construction. For each formula, precisely one of the formula, its negation, and the negation of its "is defined" formula is true on the constructed model. Many other ternary logics in the literature can be reduced to ours. Partial functions are ubiquitous in computer science and even in (in)equation solving at schools. Our work was motivated by an attempt to explain, precisely in terms of logic, typical informal methods of reasoning in such applications.Comment: 39 pages, 1 figur

Cross-border CO2 infrastructure options for a CCS demonstration in Finland

AbstractAs the geographic situation of Finland seems to allow no domestic carbon sequestration, cross-border CO2 logistics is needed. In this paper, the alternative transportation options for CO2 from a Finnish capture plant case are assessed. The assessment includes selection of the most favourable storage areas, route planning for both ship and pipeline transportation, and cost estimates for both alternatives. An actual CCS demonstration is planned by the proprietor power companies of the chosen case plant, a coal condensing power plant on the coast of Western Finland, giving an interesting opportunity to discuss the results in the light of the current development of the demonstration plant.Transportation costs are presented for a ship transportation chain from the case plant to the North Sea and for a pipeline running towards the coast of the Barents Sea. The storage areas were chosen because of the potential storage capacity and currently operational injection activities in both regions.Pipeline transportation is found considerably more expensive than ship transportation as an option for CO2 transportation from the case demonstration plant to the different storage sites. The levelized costs of shipping the captured CO2 to the geological formations under the North Sea are estimated to amount to 11,8 € /t CO2, excluding the costs for liquefaction.Matching a CO2 source within EU to a sink outside EU depends on a consistent regulatory framework. In addition to accountability of emissions allowances within the EU Emission Trading Scheme (ETS), the issues include liabilities of CO2 handling and storage, other legislation both on national and on Community level as well as international maritime conventions