Capturing Polynomial Time using Modular Decomposition

The question of whether there is a logic that captures polynomial time is one of the main open problems in descriptive complexity theory and database theory. In 2010 Grohe showed that fixed point logic with counting captures polynomial time on all classes of graphs with excluded minors. We now consider classes of graphs with excluded induced subgraphs. For such graph classes, an effective graph decomposition, called modular decomposition, was introduced by Gallai in 1976. The graphs that are non-decomposable with respect to modular decomposition are called prime. We present a tool, the Modular Decomposition Theorem, that reduces (definable) canonization of a graph class C to (definable) canonization of the class of prime graphs of C that are colored with binary relations on a linearly ordered set. By an application of the Modular Decomposition Theorem, we show that fixed point logic with counting captures polynomial time on the class of permutation graphs. Within the proof of the Modular Decomposition Theorem, we show that the modular decomposition of a graph is definable in symmetric transitive closure logic with counting. We obtain that the modular decomposition tree is computable in logarithmic space. It follows that cograph recognition and cograph canonization is computable in logarithmic space.Comment: 38 pages, 10 Figures. A preliminary version of this article appeared in the Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS '17

Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs

We show that the class of chordal claw-free graphs admits LREC$_=$-definable canonization. LREC$_=$ is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm, and therefore a logarithmic-space isomorphism test, for the class of chordal claw-free graphs. As a further consequence, LREC$_=$ captures logarithmic space on this graph class. Since LREC$_=$ is contained in fixed-point logic with counting, we also obtain that fixed-point logic with counting captures polynomial time on the class of chordal claw-free graphs.Comment: 34 pages, 13 figure

Isoperimetric Inequalities on Hexagonal Grids

We consider the edge- and vertex-isoperimetric probem on finite and infinite hexagonal grids: For a subset W of the hexagonal grid of given cardinality, we give a lower bound for the number of edges between W and its complement, and lower bounds for the number of vertices in the neighborhood of W and for the number of vertices in the boundary of W. For the infinite hexagonal grid the given bounds are tight

Sex By Deception

In this paper I will use sex by deception as a case study for highlighting some of the most tricky concepts around sexuality and moral psychology, including rape, consensual sex, sexual rights, sexual autonomy, sexual individuality, and disrespectful sex. I begin with a discussion of morally wrong sex as rooted in the breach of five sexual liberty rights that are derived from our fundamental human liberty rights: sexual self-possession, sexual autonomy, sexual individuality, sexual dignity and sexual privacy. I then argue (against the standard interpretation) that experimental findings in moral psychology show that the principle of respect for persons—a principle that grounds our human liberty rights—drives our intuitive moral judgments. In light of this discussion, I examine a puzzle about sex by deception—a puzzle which at first may seem to compel us to define 'rape' strictly in terms of force rather than sexual autonomy. I proceed by presenting an argument against the view that, as a rule, sex by deception undermines consent—a position held by prominent thinkers such as Philippe Patry (2001), Onora O’Neill (2003), Rubenfeld (2012), Tom Dougherty (2013a, 2013b), Joyce M. Short (2013), and Danielle Bromwich and Joseph Millum (2013, 2018). As we will see, sex following deception to increase your chances does not always constitute rape. Lying about your age, education, job, family background, marital status, or interest in a relationship, for example, does not make your sex partner incapable of consenting, which is to say that sex by deception need not be rape. I even go so far as to say that sex with another person that is facilitated by withholding information about having a venereal disease shouldn't be classified as rape. Although sex by deception doesn't compromise consent, it nonetheless violates the principle of respect for persons, not by vitiating sexual autonomy and compromising consent, but by failing to respect other sexual rights, such as our rights to sexual dignity, individuality, and privacy

Cooperatives, Regulation and Competition in Norwegian Agriculture

Over production is a persistent and costly problem in Norwegian agriculture. Support to agricultural production implicitly yields incentives to produce too much, i.e., causing market prices to fall below the target level, and thereby increasing the need for subsidies and additional market interventions. In order to restrict supplies, farmers are allowed to coordinate through marketing cooperatives. The paper argues that this coordination is likely to be insufficient in markets where the cooperative competes with an investor-owned wholesaler. Interventions in the market in order to remove excess supplies may induce further incentives to increase production. Levying a tax on all production in order to cover market regulation costs, moves the solution in the right direction but is impotent in restoring the target (second-best) level of production.Cooperatives, regulation, over production, duopoly, Agribusiness, Q13, L21, D43,

A unified theory of truth and reference

The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. In what follows we show that the supervaluationist approach to singular reference, when wedded to the truthmaker idea, yields a framework of surprising power, which offers a uniform set of solutions to a range of problems regarding identity, reference and knowledge, problems which have hitherto been dealt with on an ad hoc basis

Consciousness and Knowledge

This chapter focuses on the relationship between consciousness and knowledge, and in particular on the role perceptual consciousness might play in justifying beliefs about the external world. We outline a version of phenomenal dogmatism according to which perceptual experiences immediately, prima facie justify certain select parts of their content, and do so in virtue of their having a distinctive phenomenology with respect to those contents. Along the way we take up various issues in connection with this core theme, including the possibility of immediate justification, the dispute between representational and relational views of perception, the epistemic significance of cognitive penetration, the question of whether perceptual experiences are composed of more basic sensations and seemings, and questions about the existence and epistemic significance of high-level content. In a concluding section we briefly consider how some of the topics pursued here might generalize beyond perception