Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting

In this paper we study lifted inference for the Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in first-order logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the input domain; we prove that, in the first case our algorithm solves the WFOMC problem in PTIME, and in the second case it fails. Third, we present several properties of the algorithm. Finally, we discuss limitations of lifted inference for symmetric probabilistic databases (where the weights of ground literals depend only on the relation name, and not on the constants of the domain), and prove the impossibility of a dichotomy result for the complexity of probabilistic inference for the entire language FOL

Reason Maintenance - State of the Art

This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques

An Approach to Abductive Reasoning in Equational Logic

http://ijcai.org/papers13/contents.php - Posters: Constraints, Satisfiability, and Search (ijcai13.org)International audienceAbduction has been extensively studied in propositional logic because of its many applications in artificial intelligence. However, its intrinsic complexity has been a limitation to the implementation of abductive reasoning tools in more expressive logics. We have devised such a tool in ground flat equational logic, in which literals are equations or disequations between constants. Our tool is based on the computation of prime implicates. It uses a relaxed paramodulation calculus, designed to generate all prime implicates of a formula, together with a carefully defined data structure storing the implicates and able to efficiently detect, and remove, redundancies. In addition to a detailed description of this method, we present an analysis of some experimental results

Speaker meaning, what is said and what is implicated

[First Paragraph] Unlike so many other distinctions in philosophy, H P Grice's distinction between what is said and what is implicated has an immediate appeal: undergraduate students readily grasp that one who says 'someone shot my parents' has merely implicated rather than said that he was not the shooter [2]. It seems to capture things that we all really pay attention to in everyday conversation'this is why there are so many people whose entire sense of humour consists of deliberately ignoring implicatures. ('Can you pass the salt?' 'Yes.') Unsurprisingly, it was quickly picked up and put to a wide variety of uses in not only in philosophy but also in linguistics and psychology. What is surprising, however, is that upon close inspection Grice's conception of implicature turns out to be very different from those at work in the literature which has grown out of his original discussion. This would not be much of a criticism of this literature were it not for the fact that discussions of implicature explicitly claim to be using Grice's notion, not some other one inspired by him (generally going so far as to quote one of Grice's characterisations of implicature). This still would not be terribly interesting if the notion Grice was actually carving out had little theoretical or practical utility. But I will argue here that Grice's own notion of implicature, one quite different from the ones most of us have come to work with, is in fact far more interesting and subtle than that which has been attributed to him

Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin

Caultron of Unwisdom: The Legislative Offensive on Insidious Foreign Influence in the Third Term of President Vladimir V. Putin, and ICCPR Recourse for Affect Civil Advocates

Part I discusses Russian and international statutory law. It briefly outlines the structure of the government of the Russian Federation and discusses relevant articles of its Constitution. It then illustrates the legislative trend in question by discussing select legislation passed and proposed during President Putin’s third term that seeks to restrict non-Russian influence in Russian society. Part I closes with a discussion of Russia’s international human rights obligations, and the international redress available to Russian nationals affected by the laws in question. Part II considers the practical application of the laws discussed in Part I. This includes an examination of potential procedural issues relating to the complaint process a Russian national would have to navigate at one of the international human rights tribunals or treaty bodies founded under the conventions. Additionally, Part II briefly outlines international jurisprudence relevant to the prospect of Russian nationals’ success before the United Nations Human Rights Committee. Based on the interplay between the federal statutes in question and Russia’s international human rights obligations, this Note asserts in Part III that Russian nationals should file complaints to the UN Human Rights Committee. The Note also advocates for a progressive change to Russia’s domestic civil-political environment. But in the absence of such a change, individuals affected by the legislation in question can seek recourse through the Committee’s individual complaint mechanism. Those petitioning would ideally include the heads of targeted civil society and human rights monitoring and advocacy groups

A Generic Framework for Implicate Generation Modulo Theories

International audienceThe clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that generates the implicates of a quantifier-free formula modulo a theory. No assumption is made on the considered theory, other than the existence of a decision procedure. The algorithm has been implemented (using the solvers MiniSAT, CVC4 and Z3) and experimental results show evidence of the practical relevance of the proposed approach

Towards a New Account of Interpreting: Levinson’s Heuristics in the Interpretation of Press Conferences

This study refers to interpretation as a speedy and effortless process through Levinson’s utterance-type-meaning (1995, 2000). It applies Levinson’s heuristics (Q, I and M) to warrant the message accuracy and trigger the utterance meaning and function in more immediate and stereotypical manner. The heuristics were applied to the interpretation of a number of press conferences between Arabic and English. The heuristics as pragmatic principles of communication assist interpreters to produce a message that is most consistent with the speaker’s knowledge of the world or what s/he believes to be true, expand and compress the TM’s components as allocated in the SM, and communicate any reiterative, emotive, and persuasive functions through a similar level of markedness.