On the Relationships Among Quantified Autoepistemic Logic, its Kernel, and Quantified Reflective Logic

A Quantified Autoepistemic Logic is axiomatized in a monotonic Modal Quantificational Logic whose modal laws are slightly stronger than S5. This Quantified Autoepistemic Logic obeys all the laws of First Order Logic and its L predicate obeys the laws of S5 Modal Logic in every fixed-point. It is proven that this Logic has a kernel not containing L such that L holds for a sentence if and only if that sentence is in the kernel. This result is important because it shows that L is superfluous thereby allowing the ori ginal equivalence to be simplified by eliminating L from it. It is also shown that the Kernel of Quantified Autoepistemic Logic is a generalization of Quantified Reflective Logic, which coincides with it in the propositional case.

Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold.

On the Relationship between Quantified Reflective Logic and Quantified Default Logic

Reflective Logic and Default Logic are both generalized so as to allow universally quantified variables to cross modal scopes whereby the Barcan formula and its converse hold. This is done by representing both the fixed-point equation for Reflective Logic and the fixed-point equation for Default both as necessary equivalences in the Modal Quantificational Logic Z. and then inserting universal quantifiers before the defaults. The two resulting systems, called Quantified Reflective Logic and Quantified Default Logic, are then compared by deriving metatheorems of Z that express their relationships. The main result is to show that every solution to the equivalence for Quantified Default Logic is a strongly grounded solution to the equivalence for Quantified Reflective Logic. It is further shown that Quantified Reflective Logic and Quantified Default Logic have exactly the same solutions when no default has an entailment condition.

Methods for Solving Necessary Equivalences

Nonmonotonic Logics such as Autoepistemic Logic, Reflective Logic, and Default Logic, are usually defined in terms of set-theoretic fixed-point equations defined over deductively closed sets of sentences of First Order Logic. Such systems may also be represented as necessary equivalences in a Modal Logic stronger than S5 with the added advantage that such representations may be generalized to allow quantified variables crossing modal scopes resulting in a Quantified Autoepistemic Logic, a Quantified Autoepistemic Kernel, a Quantified Reflective Logic, and a Quantified Default Logic. Quantifiers in all these generalizations obey all the normal laws of logic including both the Barcan formula and its converse. Herein, we address the problem of solving some necessary equivalences containing universal quantifiers over modal scopes. Solutions obtained by these methods are then compared to related results obtained in the literature by Circumscription in Second Order Logic since the disjunction of all the solutions of a necessary equivalence containing just normal defaults in these Quantified Logics, is equivalent to that system.

Tipos de lógica utilizadas en la toma de decisiones estratégicas de marketing

Para el administrador el proceso de la toma de decisiones es uno de sus mayores retos y responsabilidades, ya que en su desarrollo se debe definir el camino más acertado en un sin número de alternativas, teniendo en cuenta los obstáculos sociales, políticos y económicos del entorno empresarial. Para llegar a la decisión adecuada no hay que perder de vista los objetivos y metas propuestas, además de tener presente el proceso lógico, detectando, analizando y demostrando el porqué de esa elección. Consecuentemente el análisis que propone esta investigación aportara conocimientos sobre los tipos de lógica utilizados en la toma de decisiones estratégicas al administrador para satisfacer las demandas asociadas con el mercadeo para que de esta manera se pueda generar y ampliar eficientemente las competencia idóneas del administrador en la inserción internacional de un mercado laboral cada vez mayor (Valero, 2011). A lo largo de la investigación se pretende desarrollar un estudio teórico para explicar la relación entre la lógica y la toma de decisiones estratégicas de marketing y como estos conceptos se combinan para llegar a un resultado final. Esto se llevara a cabo por medio de un análisis de planes de marketing, iniciando por conceptos básicos como marketing, lógica, decisiones estratégicas, dirección de marketing seguido de los principios lógicos y contradicciones que se pueden llegar a generar entre la fundamentación teórica

Semantics of logic programs with explicit negation

After a historical introduction, the bulk of the thesis concerns the study of a declarative semantics for logic programs. The main original contributions are: ² WFSX (Well–Founded Semantics with eXplicit negation), a new semantics for logic programs with explicit negation (i.e. extended logic programs), which compares favourably in its properties with other extant semantics. ² A generic characterization schema that facilitates comparisons among a diversity of semantics of extended logic programs, including WFSX. ² An autoepistemic and a default logic corresponding to WFSX, which solve existing problems of the classical approaches to autoepistemic and default logics, and clarify the meaning of explicit negation in logic programs. ² A framework for defining a spectrum of semantics of extended logic programs based on the abduction of negative hypotheses. This framework allows for the characterization of different levels of scepticism/credulity, consensuality, and argumentation. One of the semantics of abduction coincides with WFSX. ² O–semantics, a semantics that uniquely adds more CWA hypotheses to WFSX. The techniques used for doing so are applicable as well to the well–founded semantics of normal logic programs. ² By introducing explicit negation into logic programs contradiction may appear. I present two approaches for dealing with contradiction, and show their equivalence. One of the approaches consists in avoiding contradiction, and is based on restrictions in the adoption of abductive hypotheses. The other approach consists in removing contradiction, and is based in a transformation of contradictory programs into noncontradictory ones, guided by the reasons for contradiction.

Implementation of multiple specialization in logic programs

We study the múltiple specialization of logic programs based on abstract interpretation. This involves in general generating several versions of a program predícate for different uses of such predícate, making use of information obtained from global analysis performed by an abstract interpreter, and finally producing a new, "multiply specialized" program. While the topic of múltiple specialization of logic programs has received considerable theoretical attention, it has never been actually incorporated in a compiler and its effects quantified. We perform such a study in the context of a parallelizing compiler and show that it is indeed a relevant technique in practice. Also, we propose an implementation technique which has the same power as the strongest of the previously proposed techniques but requires little or no modification of an existing abstract interpreter.

Representing "Recursive" Default Logic in Modal Logic

The "recursive" definition of Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the "recursive" fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning of the fixed-point is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original "recursive" definition of Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults.

Representing Reflective Logic in Modal Logic

The nonmonotonic logic called Reflective Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Reflective Logic with an initial set of axioms and defaults if and only if the meaning of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Reflective Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since all the laws of First Order Logic hold and since both the Barcan Formula and its converse hold.

Representing Default Logic in Modal Logic

The nonmonotonic logic called Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan Formula and its converse hold.

A classification methodology for the risk of weed infestation using fuzzy logic

Despite modern weed control practices, weeds continue to be a threat to agricultural production. Considering the variability of weeds, a classification methodology for the risk of infestation in agricultural zones using fuzzy logic is proposed. The inputs for the classification are attributes extracted from estimated maps for weed seed production and weed coverage using kriging and map analysis and from the percentage of surface infested by grass weeds, in order to account for the presence of weed species with a high rate of development and proliferation. The output for the classification predicts the risk of infestation of regions of the field for the next crop. The risk classification methodology described in this paper integrates analysis techniques which may help to reduce costs and improve weed control practices. Results for the risk classification of the infestation in a maize crop field are presented. To illustrate the effectiveness of the proposed system, the risk of infestation over the entire field is checked against the yield loss map estimated by kriging and also with the average yield loss estimated from a hyperbolic model.

Dweller perception using fuzzy logic for slum upgrading

A large number of initiatives in cities in Brazil - including slum clearance and upgrading - have been undertaken over the years in an effort to ameliorate the problems arising from informal occupation; unfortunately, however, little is known about the related performance outcomes. Careful appraisal of the results of such initiatives is thus called for, covering evaluations of dwellers` perceptions of the upgraded environments. Among the available evaluation methods, post-occupancy evaluation (POE) is commonly employed, although it fails adequately to reflect prevailing subjective concepts of quality. The present paper contains the partial findings of a research exercise aimed at developing an original method, using fuzzy logic, for urban environmental quality evaluation in informally occupied areas on the basis of combining quantitative indicators and dweller perception. It combines POE with fuzzy logic in order to develop tools that can better model the uncertain information that emerges from that kind of study. This paper aims to introduce an uncertainty measure used in order to identify the strengths and weaknesses of slum upgrading projects. The results show that it is possible to quantify certainty degrees in the findings and to define if additional information is needed.

Expert system for the assessment of power transformer insulation condition based on type-2 fuzzy logic systems

An efficient expert system for the power transformer condition assessment is presented in this paper. Through the application of Duval`s triangle and the method of the gas ratios a first assessment of the transformer condition is obtained in the form of a dissolved gas analysis (DGA) diagnosis according IEC 60599. As a second step, a knowledge mining procedure is performed, by conducting surveys whose results are fed into a first Type-2 Fuzzy Logic System (T2-FLS), in order to initially evaluate the condition of the equipment taking only the results of dissolved gas analysis into account. The output of this first T2-FLS is used as the input of a second T2-FLS, which additionally weighs up the condition of the paper-oil system. The output of this last T2-FLS is given in terms of words easily understandable by the maintenance personnel. The proposed assessing methodology has been validated for several cases of transformers in service. (C) 2010 Elsevier Ltd. All rights reserved.

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments. (C) 2007 Elsevier B.V. All rights reserved.

Probabilistic logic with independence

This paper investigates probabilistic logics endowed with independence relations. We review propositional probabilistic languages without and with independence. We then consider graph-theoretic representations for propositional probabilistic logic with independence; complexity is analyzed, algorithms are derived, and examples are discussed. Finally, we examine a restricted first-order probabilistic logic that generalizes relational Bayesian networks. (c) 2007 Elsevier Inc. All rights reserved.