Logic Programming as Constructivism

The features of logic programming that seem unconventional from the viewpoint of classical logic can be explained in terms of constructivistic logic. We motivate and propose a constructivistic proof theory of non-Horn logic programming. Then, we apply this formalization for establishing results of practical interest. First, we show that 'stratification can be motivated in a simple and intuitive way. Relying on similar motivations, we introduce the larger classes of 'loosely stratified' and 'constructively consistent' programs. Second, we give a formal basis for introducing quantifiers into queries and logic programs by defining 'constructively domain independent* formulas. Third, we extend the Generalized Magic Sets procedure to loosely stratified and constructively consistent programs, by relying on a 'conditional fixpoini procedure

EF+EX Forest Algebras

We examine languages of unranked forests definable using the temporal operators EF and EX. We characterize the languages definable in this logic, and various fragments thereof, using the syntactic forest algebras introduced by Bojanczyk and Walukiewicz. Our algebraic characterizations yield efficient algorithms for deciding when a given language of forests is definable in this logic. The proofs are based on understanding the wreath product closures of a few small algebras, for which we introduce a general ideal theory for forest algebras. This combines ideas from the work of Bojanczyk and Walukiewicz for the analogous logics on binary trees and from early work of Stiffler on wreath product of finite semigroups

An Abstract Machine for Unification Grammars

This work describes the design and implementation of an abstract machine, Amalia, for the linguistic formalism ALE, which is based on typed feature structures. This formalism is one of the most widely accepted in computational linguistics and has been used for designing grammars in various linguistic theories, most notably HPSG. Amalia is composed of data structures and a set of instructions, augmented by a compiler from the grammatical formalism to the abstract instructions, and a (portable) interpreter of the abstract instructions. The effect of each instruction is defined using a low-level language that can be executed on ordinary hardware. The advantages of the abstract machine approach are twofold. From a theoretical point of view, the abstract machine gives a well-defined operational semantics to the grammatical formalism. This ensures that grammars specified using our system are endowed with well defined meaning. It enables, for example, to formally verify the correctness of a compiler for HPSG, given an independent definition. From a practical point of view, Amalia is the first system that employs a direct compilation scheme for unification grammars that are based on typed feature structures. The use of amalia results in a much improved performance over existing systems. In order to test the machine on a realistic application, we have developed a small-scale, HPSG-based grammar for a fragment of the Hebrew language, using Amalia as the development platform. This is the first application of HPSG to a Semitic language.Comment: Doctoral Thesis, 96 pages, many postscript figures, uses pstricks, pst-node, psfig, fullname and a macros fil

Quantum value indefiniteness

The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum alone. We discuss possible interpretations and consequences for quantum oracles.Comment: 19 pages, 2 tables, 2 figures; contribution to PC0