Why Philosophers Should Care About Computational Complexity

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and beyond," MIT Press, 2012. Some minor clarifications and corrections; new references adde

Magic sets with full sharing

In this paper we study the relationship between tabulation and goal-oriented bottom-up evaluation of logic programs. Differences emerge when one tries to identify features of one evaluation method in the other. We show that to obtain the same effect as tabulation in top-down evaluation, one has to perform a careful {\em adornment} in programs to be evaluated bottom-up. Furthermore we propose an efficient algorithm to perform forward subsumption che cking over adorned {\em magic facts}

The efficient evaluation of visual queries within a logic-based framework

Bibliography: leaves 149-153.There has been much research in the area of visual query systems in recent years. This has stemmed from the need for a more powerful database visualization and querying ability. In addition, there has been a pressing need for a more intuitive interface for the non-expert user. Systems such as Hy+, developed at the University of Toronto, provide environments that satisfy a wide range of database interaction and querying, with the advantage of maintaining a visual interface abstraction throughout. This thesis explores issues related to the translation and evaluation of visual queries, including semantic and optimization possibilities. The primary focus will be on the GraphLog query language, defined in the context of the Hy+ visualization system. GraphLog is translated to the deductive database language Datalog, which is subsequently evaluated by the CORAL logic database system. We propose graph semantics, which define the meaning of visual queries in terms of paths in a graph, for monotone GraphLog. This provides a more intuitive meaning which is not linked to any particular translation. Therefore, Datalog generated by a translation may be compared to well-defined semantics to ensure that the translation preserves the intended meaning. By examining various queries in terms of the graph semantics, we uncover a shortcoming in the existing GraphLog translation. In addition, an alternative translation to Datalog, based on the construction of a nondeterministic finite state automaton, is described for GraphLog queries. The translation has the property that visual queries containing constants are optimized using a technique known as factoring. In addition, the translation performs an optimization on queries with multiple edges that contain no constants, referred to here as variable constraining

Centre for Information Science Research Annual Report, 1987-1991

Annual reports from various departments of the AN

Logical Foundations of Object-Oriented and Frame-Based Languages

We propose a novel logic, called Frame Logic (abbr., F-logic), that accounts in a clean, declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the object-oriented paradigm as classical predicate calculus stands to relational programming. The syntax of F-logic is higher-order, which, among other things, allows the user to explore data and schema using the same declarative language. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof procedure. This paper also discusses various aspects of programming in declarative object-oriented languages based on F-logic

February 9, 2018 Meeting Minutes

Minutes of the February 9, 2018 Board of Trustees meeting

Deciding Second-order Logics using Database Evaluation Techniques

We outline a novel technique that maps the satisfiability problems of second-order logics, in particular WSnS (weak monadic second-order logic with n successors), S1S (monadic second-order logic with one successor), and of μ-calculus, to the problem of query evaluation of Complex-value Datalog queries. In this dissertation, we propose techniques that use database evaluation and optimization techniques for automata-based decision procedures for the above logics. We show how the use of advanced implementation techniques for Deductive databases and for Logic Programs, in particular the use of tabling, yields a considerable improvement in performance over more traditional approaches. We also explore various optimizations of the proposed technique, in particular we consider variants of tabling and goal reordering. We then show that the decision problem for S1S can be mapped to the problem of query evaluation of Complex-value Datalog queries. We explore optimizations that can be applied to various types of formulas. Last, we propose analogous techniques that allow us to approach μ-calculus satisfiability problem in an incremental fashion and without the need for re-computation. In addition, we outline a top-down evaluation technique to drive our incremental procedure and propose heuristics that guide the problem partitioning to reduce the size of the problems that need to be solved

Efficient Semiring-Weighted Earley Parsing

This paper provides a reference description, in the form of a deduction system, of Earley's (1970) context-free parsing algorithm with various speed-ups. Our presentation includes a known worst-case runtime improvement from Earley's $O (N^3|G||R|)$, which is unworkable for the large grammars that arise in natural language processing, to $O (N^3|G|)$, which matches the runtime of CKY on a binarized version of the grammar $G$. Here $N$ is the length of the sentence, $|R|$ is the number of productions in $G$, and $|G|$ is the total length of those productions. We also provide a version that achieves runtime of $O (N^3|M|)$ with $|M| \leq |G|$ when the grammar is represented compactly as a single finite-state automaton $M$ (this is partly novel). We carefully treat the generalization to semiring-weighted deduction, preprocessing the grammar like Stolcke (1995) to eliminate deduction cycles, and further generalize Stolcke's method to compute the weights of sentence prefixes. We also provide implementation details for efficient execution, ensuring that on a preprocessed grammar, the semiring-weighted versions of our methods have the same asymptotic runtime and space requirements as the unweighted methods, including sub-cubic runtime on some grammars.Comment: Main conference long paper at ACL 202