Marisa Navarro

A two-stage classifier for broken and blurred digits in forms

A classifier for an automatic system that recognizes multifont typewritten digits, often broken and blurred, in forms is presented. The classification, which is based on the utilization of a global feature, is applied in two phases. Firstly, a minimum distance method (1-NN) is applied in a multifont classifier to provide a global classification of the patterns in a form. A problem associated to multifont classifiers is the interference among classes in different fonts. An interesting aspect of this particular application is that it is highly probable that a form includes just one font. Then, in the second phase, a specialized classifier, oriented to one-form, uses the patterns in the form previously classified to validate, or reject and reclassify them, on the basis of the mean distance to the predefined classes. This specialized classifier affords significant improvement in performance. A classification accuracy rate of 99.42% has been achieved.

On the correctness of modular systems

Given a requirements specification for a software system, a simple (modular) software development process can be represented by a tree, as follows: Here, the (informal or semi-formal) requirements specification is transformed into a detailed (formal) specification consisting of the specification modules M1,..., Mn. Then, the development phase starts and each of the specification modules is refined into a new set of modules. The process continues until all the specification modules describe objects that can be directly coded in the given programming language, obtaining as a result the set of program modules Pi1,..., Pik. Modular correctness means that the set of program modules Pi1,..., Pik should be a correct implementation of the given system if every refinement step applied to any module is correct.

A cut-free and invariant-free sequent calculus for PLTL

Sequent calculi usually provide a general deductive setting that uniformly embeds other proof-theoretical approaches, such as tableaux methods, resolution techniques, goal-directed proofs, etc. Unfortunately, in temporal logic, existing sequent calculi make use of a kind of inference rules that prevent the effective mechanization of temporal deduction in the general setting. In particular, temporal sequent calculi either need some form of cut, or they make use of invariants, or they include infinitary rules. This is the case even for the simplest kind of temporal logic, propositional linear temporal logic (PLTL). In this paper, we provide a complete finitary sequent calculus for PLTL, called FC, that not only is cut-free but also invariant-free. In particular, we introduce new rules which provide a new style of temporal deduction. We give a detailed proof of completeness.

Systematic Semantic Tableaux for PLTL

The better known methods of semantic tableaux for deciding satisfiability in propositional linear temporal logic generate graphs in addition to classical trees. The test of satisfaction is made from the graph and it does not correspond with the application of rules in any calculus for PLTL. We present here a new method of semantic tableaux without using additional graphs. The method is based on a new complete finitary sequent calculus for PLTL which allows us to incorporate all the information in a tree. This approach makes our tableaux better suited for completely automatic theorem proving.

Dual systems of tableaux and sequents for PLTL

Abstract On one hand, traditional tableau systems for temporal logic (TL) generate an auxiliary graph that must be checked and (possibly) pruned in a second phase of the refutation procedure. On the other hand, traditional sequent calculi for TL make use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automatization. A remarkable consequence of using auxiliary graphs in the tableaux framework and invariants or infinitary rules in the sequents framework is that TL fails to carry out the classical correspondence between tableaux and sequents. In this paper, we first provide a tableau method TTM that does not require auxiliary graphs to decide whether a set of PLTL-formulas is satisfiable. This tableau method TTM is directly associated to a one-sided sequent calculus called TTC. Since TTM is free from all the structural rules that hinder the mechanization of deduction, e.g. weakening and contraction, then the resulting sequent calculus TTC is also free from this kind of structural rules. In particular, TTC is free of any kind of cut, including invariant-based cut. From the deduction system TTC, we obtain a two-sided sequent calculus GTC that preserves all these good freeness properties and is finitary, sound and complete for PTL. Therefore, we show that the classical correspondence between tableaux and sequent calculi can be extended to TL. Every deduction system is proved to be complete. In addition, we provide illustrative examples of deductions in the different systems.

A Strong Logic Programming View for Static Embedded Implications

A strong (L) logic programming language ([14, 15]) is given by two subclasses of formulas (programs and goals) of the underlying logic L, provided that: firstly, any program P (viewed as a L-theory) has a canonical model MP which is initial in the category of all its L-models; secondly, the L-satisfaction of a goal G in MP is equivalent to the L-derivability of G from P, and finally, there exists an effective (computable) proof-subcalculus of the L-calculus which works out for derivation of goals from programs. In this sense, Horn clauses constitute a strong (first-order) logic programming language. Following the methodology suggested in [15] for designing logic programming languages, an extension of Horn clauses should be made by extending its underlying first-order logic to a richer logic which supports a strong axiomatization of the extended logic programming language. A well-known approach for extending Horn clauses with embedded implications is the static scope programming language presented in [8]. In this paper we show that such language can be seen as a strong FO⊃ logic programming language, where FO⊃ is a very natural extension of first-order logic with intuitionistic implication. That is, we present a new characterization of the language in [8] which shows that Horn clauses extended with embedded implications, viewed as FO⊃-theories, preserves all the attractive mathematical and computational properties that Horn clauses satisfy as first-order-theories.

Implementation and Behavioural Equivalence: A Survey

In this paper we try to shed some light over the similarities and differences among the different approaches to define implementations and behavioural equivalence. For obvious reasons, we do not discuss all existing approaches individually. However a formal framework is used to discuss the most important ones. Additionally, some issues concerning implementations that in our opinion are often misunderstood, especially transitivity of implementation correctness and its role in the software development process, are discussed in detail.

On the Equivalence of Hierarchical and Non-Hierarchical Rewriting on Conditional Term Rewriting Systems

To avoid certain specific problems (concerning termination) of conditional term rewriting systems, most of the authors cited above work. with, the so-called, hierarchical rewriting~ the systems are defined it, a hierarchical mar, r, er (by successive enrichments), the conditior, part of a giver, rule should only involve terms of lower hierarchy level, and, finally, when applying a rule the variables occurring in the condition may only be instantiated by terms of lower hierarchy~ This should guarantee to avoid the circularity problems that may appear on the evaluation of the conditions.

Invariant-Free Clausal Temporal Resolution

Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires to generate invariants for performing resolution on eventualities. The methods and techniques developed in that approach have also been successfully adapted in order to obtain a clausal resolution method for Computation Tree Logic (CTL), but invariant handling seems to be a handicap for further extension to more general branching temporal logics. In this paper, we present a new approach to applying resolution to PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Hence, we say that the approach presented in this paper is invariant-free. Our method is based on the dual methods of tableaux and sequents for PLTL that we presented in a previous paper. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called trs-resolution, that extends classical propositional resolution. Finally, we prove that trs-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL.

Segmentation of low-quality typewritten digits

This work addresses the segmentation of numeric fields in forms presenting blurring, breaks and touching in digits. In an OCR system, the segmentation phase plays a determinant role in the global accuracy of the system. Segmentation is basically addressed from two approaches: (a) as an isolated phase in the OCR process, and (b) as interacting with the recognition of the segmented item. In this work, we have considered the first one in order to develop a robust new cost function combining vertical projection, Tsujimoto metric (1991) and background information. Unlike other techniques reported in the literature, ours obtains a near-optimum number of break points in fields containing broken, blurred and touching characters, leading to high accuracy in the global OCR system. Our experiments with a sample including about 11283 numeric fields in 144 forms (more than 50000 digits of that kind) show that 99.74% of fields have been correctly segmented. The new cost function only made 50 errors.