114,406 research outputs found

    Trading inference effort versus size in CNF Knowledge Compilation

    Full text link
    Knowledge Compilation (KC) studies compilation of boolean functions f into some formalism F, which allows to answer all queries of a certain kind in polynomial time. Due to its relevance for SAT solving, we concentrate on the query type "clausal entailment" (CE), i.e., whether a clause C follows from f or not, and we consider subclasses of CNF, i.e., clause-sets F with special properties. In this report we do not allow auxiliary variables (except of the Outlook), and thus F needs to be equivalent to f. We consider the hierarchies UC_k <= WC_k, which were introduced by the authors in 2012. Each level allows CE queries. The first two levels are well-known classes for KC. Namely UC_0 = WC_0 is the same as PI as studied in KC, that is, f is represented by the set of all prime implicates, while UC_1 = WC_1 is the same as UC, the class of unit-refutation complete clause-sets introduced by del Val 1994. We show that for each k there are (sequences of) boolean functions with polysize representations in UC_{k+1}, but with an exponential lower bound on representations in WC_k. Such a separation was previously only know for k=0. We also consider PC < UC, the class of propagation-complete clause-sets. We show that there are (sequences of) boolean functions with polysize representations in UC, while there is an exponential lower bound for representations in PC. These separations are steps towards a general conjecture determining the representation power of the hierarchies PC_k < UC_k <= WC_k. The strong form of this conjecture also allows auxiliary variables, as discussed in depth in the Outlook.Comment: 43 pages, second version with literature updates. Proceeds with the separation results from the discontinued arXiv:1302.442

    Numerical study of the urban geometrical representation impact in a surface energy budget model

    Get PDF
    The aim of this work is to investigate how both the orientation of the urban canyon and the modeling of the edge effects (i.e. urban canyons of finite length) are important in the numerical simulation of the surface energy budget in urban areas. Starting from the town energy balance scheme, two models of increasing complexity of the canyon geometry are developed. A sensitivity analysis of the role played by the chosen hypothesis and parameterizations is performed by coupling the canyon schemes with the numerical weather prediction model RAMS. The results suggest that a detailed description of the urban geometry could produce non-negligible differences of the energy balances and of the temperature fields with respect to what occurs using simpler schematizations, in particular during the summer

    Scientia intuitiva in the Ethics

    Get PDF
    **For my more recent views of the third kind of cognition, see my "Finding Oneself in God"** Abstract: Cognition of the third kind, or scientia intuitiva, is supposed to secure beatitudo, or virtue itself (E5p42). But what is scientia intuitiva, and how is it different from (and superior to) reason? I suggest a new answer to this old and vexing question at the core of Spinoza’s project in the Ethics. On my view, Spinoza’s scientia intuitiva resembles Descartes’s scientia more than has been appreciated. Although Spinoza’s God is not Descartes’s benevolent, transcendent God, Spinoza agrees with Descartes that the highest certainty requires that a cognizer correctly conceive of God and her causal relation to God; it is only with cognition of the third kind that a cognizer can be certain that her adequate (that is, clear and distinct) representations of extramental things agree with formally real, extramental ideata, and so are true. If this is right, a reading of Spinoza that has dominated scholarship since the Ethics’ publication is misguided: for Spinoza, it is not always the case that having (and recognizing that one has) a clear and distinct idea is sufficient for knowing that that idea is true. I end the chapter by suggesting why scientia is intuitive for Spinoza: Spinoza attempts to avoid Cartesian-Circle-style circularity by insisting that a cognizer must intuit the correct representation of God and God’s relation to things

    Quantum Structures: An Attempt to Explain the Origin of their Appearance in Nature

    Get PDF
    We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement process. We present a quantum machine, where we can illustrate in a simple way how the quantum structure arises as a consequence of the two mentioned effects. We introduce a parameter epsilon that measures the size of the lack of knowledge on the measurement process, and by varying this parameter, we describe a continuous evolution from a quantum structure (maximal lack of knowledge) to a classical structure (zero lack of knowledge). We show that for intermediate values of epsilon we find a new type of structure, that is neither quantum nor classical. We apply the model that we have introduced to situations of lack of knowledge about the measurement process appearing in other regions of reality. More specifically we investigate the quantum-like structures that appear in the situation of psychological decision processes, where the subject is influenced during the testing, and forms some of his opinions during the testing process. Our conclusion is that in the light of this explanation, the quantum probabilities are epistemic and not ontological, which means that quantum mechanics is compatible with a determinism of the whole.Comment: 22 pages, 8 figure
    • …
    corecore