Regular path expressions in feature logic

We examine the existential fragment of a feature logic, which is extended by regular path expressions. A regular path expression is a subterm relation, where the allowed paths for the subterms are restricted to any given regular language. We will prove that satisfiability is decidable. This is achieved by setting up a quasi-terminating rule system

How to win a game with features

We show, that the axiomatization of rational trees in the language of features given elsewhere is complete. In contrast to other completeness proofs that have been given in this field, we employ the method of Ehrenfeucht-Fraïssé Games, which yields a much simpler proof. The result extends previous results on complete axiomatizations of rational trees in the language of constructor equations or in a weaker feature language

A Complete and Recursive Feature Theory

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions considered in this paper are the possibly quantified first-order formulae obtained from a signature of binary and unary predicates called features and sorts, respectively. We establish a first-order theory FT by means of three axiom schemes, show its completeness, and construct three elementarily equivalent models. One of the models consists of so-called feature graphs, a data structure common in computational linguistics. The other two models consist of so-called feature trees, a record-like data structure generalizing the trees corresponding to first-order terms. Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified feature descriptions.Comment: Short version appeared in the 1992 Annual Meeting of the Association for Computational Linguistic

A complete axiomatization of a theory with feature and arity constraints

CFT is a recent constraint system providing records as a logical data structure for logic programming and for natural language processing. It combines the rational tree system as defined for logic programming with the feature tree system as used in natural language processing. The formulae considered in this paper are all first-order-logic formulae over a signature of binary and unary predicates called features and arities, respectively. We establish the theory CFT by means of seven axiom schemes and show its completeness. Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified record descriptions

CPSP-tools – Exact and complete algorithms for high-throughput 3D lattice protein studies

<p>Abstract</p> <p>Background</p> <p>The principles of protein folding and evolution pose problems of very high inherent complexity. Often these problems are tackled using simplified protein models, e.g. lattice proteins. The CPSP-tools package provides programs to solve exactly and completely the problems typical of studies using 3D lattice protein models. Among the tasks addressed are the prediction of (all) globally optimal and/or suboptimal structures as well as sequence design and neutral network exploration.</p> <p>Results</p> <p>In contrast to stochastic approaches, which are not capable of answering many fundamental questions, our methods are based on fast, non-heuristic techniques. The resulting tools are designed for high-throughput studies of 3D-lattice proteins utilising the Hydrophobic-Polar (HP) model. The source bundle is freely available <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p> <p>Conclusion</p> <p>The CPSP-tools package is the first set of exact and complete methods for extensive, high-throughput studies of non-restricted 3D-lattice protein models. In particular, our package deals with cubic and face centered cubic (FCC) lattices.</p

Unifying evolutionary and thermodynamic information for RNA folding of multiple alignments

Computational methods for determining the secondary structure of RNA sequences from given alignments are currently either based on thermodynamic folding, compensatory base pair substitutions or both. However, there is currently no approach that combines both sources of information in a single optimization problem. Here, we present a model that formally integrates both the energy-based and evolution-based approaches to predict the folding of multiple aligned RNA sequences. We have implemented an extended version of Pfold that identifies base pairs that have high probabilities of being conserved and of being energetically favorable. The consensus structure is predicted using a maximum expected accuracy scoring scheme to smoothen the effect of incorrectly predicted base pairs. Parameter tuning revealed that the probability of base pairing has a higher impact on the RNA structure prediction than the corresponding probability of being single stranded. Furthermore, we found that structurally conserved RNA motifs are mostly supported by folding energies. Other problems (e.g. RNA-folding kinetics) may also benefit from employing the principles of the model we introduce. Our implementation, PETfold, was tested on a set of 46 well-curated Rfam families and its performance compared favorably to that of Pfold and RNAalifold

A first-order axiomatization of the theory of finite trees

We provide first-order axioms for the theories of finite trees with bounded branching and finite trees with arbitrary (finite) branching. The signature is chosen to express, in a natural way, those properties of trees most relevant to linguistic theories. These axioms provide a foundation for results in linguistics that are based on reasoning formally about such properties. We include some observations on the expressive power of these theories relative to traditional language complexity classes