Nonmonotonic Logic

We present a logical framework for modeling and reasoning about the evolution of requirements. We demonstrate how a sufficiently rich meta level logic can formally capture intuitive aspects of managing changes to requirements models, while maintaining completeness and consistency. We consider a theory as the deductive closure of a given set of axioms and conclude that software engineering is concerned, in essence, with, building and managing large theories. This theory construction commences with the development of the requirements model which we view as a theory of some nonmonotonic logic. Requirements evolution then involves the mapping of one such theory to another. Exploiting the deductive power of the theory of belief revision and nonmonotonic reasoning we develop a formal description of this mapping, as well as the requirements engineering process itself. This work thus offers a rigorous approach to reasoning about requirements evolution and a important focus for defining semantically well founded methods and tools for the effective management of changing requirements

Después de más de treinta años, en esta página se expone mi primer intento de tesis de doctorado, un texto maldito que ha llegado a ser legendario por las buenas y las malas razones y cuya existencia misma se ha puesto alguna vez en tela de juicio. Contrariamente a los mitos urbanos que se han echado a rodar, la tesis nunca fue desaprobada. Nunca fue aprobada tampoco, ya que simplemente rechacé haciendo abandono del campo (y por las razones cuyo fundamento acompaño) un  puñado de observaciones que dos de mis tres evaluadores echaron al aire sin que se labrase ningún acta protocolar. Observaciones que tanto tiempo después, ahora ya no  tanto desde el llano, sigo encontrando más insustanciales cada día que pasa.

Después de una virtual cancelación a principios de los años 90, la Inteligencia Artificial se muestra hoy no tanto como la especialización de nicho que muchos creen que es, sino como componente irreductible de las tecnologías complejas de primera línea. Todos saben que la programación lógico del modo GOFAI (Good Old Fashioned Artificial Intelligence) no es el único jugador en la arena tecnológica. Yo bien lo sabía ya entonces. Pero sin duda es un aspecto importante de las tácticas de hoy en día y pinta con serlo cada vez más.

Lo que me resulta más significativo al cabo del tiempo es que el motor de inferencia de uno de los modelos más característicos que yo desarrollé (y que usé para motorizar una base de datos de identificación de estilos cerámicos de América Precolombina) fue utilizado por médicos del Hospital de Niños de la ciudad de Buenos Aires concentrados en torno de la red PCCP como sistema experto de diagnóstico clínico durante años sin que yo tuviera que cambiar una coma.

El segundo elemento de juicio más significativo concierne a que toda la trayectoria de uno de mis jurados contumaces elaboró su carrera tardía en materia de lógica no monotónica en base a observaciones y a terminología técnica que yo desarrollé con algún detenimiento en el curso de la tesis. Algún día elaboraré el detalle de estos acontecimientos porque hacen al modus operandi de los detractores antiguos y (pos)modernos en el campo de las ciencias cognitivas. Nadie se arriesga a que en materia de predicciones tecnológicas la ciencia acabe pasándonos por encima.

Este artigo discute o uso de simulações de computador em Epistemologia(Epistemologia Computacional). O objetivo o artigo é fundamentar e discu-tir a ideia de uma Epistemologia Computacional, além de apresentar umexemplo de estudo nesse campo. Na Introdução, discuto as objeções maiscomuns aos métodos da Epistemologia Tradicional e à proposta de Quine deuma Epistemologia Naturalizada. Argumento que a Epistemologia Compu-tacional não está sujeita a nenhuma destas objeções. Na Seção 1, apresentouma revisão bibliográfica dos estudos em Epistemologia Computacional(tanto em Epistemologia individualista quanto em Epistemologia Social) ediscuto a estrutura geral destes estudos. Na Seção 2, apresento alguns resul-tados de um estudo em Epistemologia Computacional que realizei em minhatese de doutorado.

ENGLISH: This paper is about the use of computer simulations in Epistemology (Com- putational Epistemology). The goal of the paper is to ground and discuss theidea of a Computational Epistemology, and to present an example of studyin this field. In the Introduction, I discuss the most common objections tothe methods of Traditional Epistemology and to Quine’s Naturalized Episte-mology. I argue that Computation Epistemology is not subject to any of the-se objections. In Section 1, I review the literature on Computational Episte-mology (both in individualistic Epistemology and in Social Epistemology)and discuss the general structure of these studies. In Section 2, I presentsome results of my PhD dissertation on Computational Epistemology.

Defeasible logic (DL) has attracted significant attention in nonmonotonic reasoning and found many applications, particularly in expert systems and knowledge-based systems communities. Even though backward chaining DL reasoners are mature enough to deal with real-life applications by supporting first-order form of the logic, the forward chaining reasoners of this logic programs only adopt propositional form. To address the problem, this paper proposes and evaluates a grounder system for stratified defeasible logic programs specialized for the SPINdle defeasible logic reasoner. Our method combines approaches from dlv and gringo grounders accompanied with a developed indexer and stratification modules for the reasoner. Our experimental results indicate that the system is able to deal with millions of facts generated based on the web data model efficiently. To the best of our knowledge, this system is the first grounder developed for forward chaining DL reasoning approach.

Nonmonotonic reasoning allows—contrary to classical (monotone) logic—for withdrawing conclusions in the light of new evidence. Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. system p is a central, broadly accepted nonmonotonic reasoning system that proposes basic rationality postulates for reasoning about nonmonotonic conditionals. Nonmonotonic conditionals are “if–then” relations for the ...

Pavel Florensky (1882-1937), a Russian theologian, philosopher , and mathematician, argued that the religious discourse is essentially contradictory and put forward the idea of the logical theory of antino-mies. Recently his views raised interesting discussions among logicians who consider him a forerunner of many non-classical logics. In this paper I discuss four interpretations of Florensky's views: paraconsistent, L-contradictory, non-monotonic and rhetorical. In conclusion I argue for the integral interpretation which unites these four approaches. Mathematics Subject Classification. Primary 03A05; Secondary 03B65, 03B42, 03B53.

W pracy Logiczna analiza operacji zdefiniowanych w trzech konstrukcjach Makinsona (Łukowski 2013) został zakwestionowany niemonotoniczny charakter operacji trzech typów zaproponowanych przez Davida Makinsona w jego książce Bridges from Classical to Nonmonotonic Logic (2005). Precyzyjna, logiczna analiza trzech kolejnych konstrukcji pokazuje, że jedynie druga określa operacje (relacje) spełniające definicję inferencji niemonotonicznej. Trudno jest jednak odmówić wartości tym konstrukcjom; co więcej, jest ona dość wysoka. Aby ją dostrzec, należy jednak odrzucić niemonotoniczną perspektywę postrzegania tych operacji. Okazuje się wówczas, że mają one wiele wspólnego z naszym codziennym myśleniem. Każda konstrukcja formalizuje inny sposób rozumowania, które jest nam jednak bardzo bliskie. Niniejsza praca, będąc kontynuacją wspomnianego wyżej artykułu, stanowi propozycję innego, kognitywno-psychologicznego spojrzenia na wartościową propozycję Makinsona. Zaproponowana tu interpretacja odwołuje się do ustaleń psychologii poznawczej i nie ma nic wspólnego z niemonotonicznością.

Conjunction fallacies (CF) have not only been a major obstacle in justifying the rationality of a Bayesian theory of belief update; they have also inspired a variety of theories on probability judgment and logical predication. Here we provide an overview of Bayesian logic (BL) as rational formulation of a pattern-based class of conjunction fallacies. BL is described here as a generalization of Bayesian Occam's razor. BL captures the idea that probabilities are sometimes used not extensionally but intensionally, determining the probabilistic adequacy of ideal logical patterns. It is emphasized that BL is a class of models that depend on representations and the meanings of logical connectives. We discuss open questions and limits of BL. We also briefly discuss whether other theories of the CF may be good supplementary theories of CFs (and predication) as well, if linked to functional explanations.

In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.

Building theories of organizations is challenging: theories are partial and "folk" categories are fuzzy. The commonly used tools--first-order logic and its foundational set theory--are ill-suited for handling these complications. Here, three leading authorities rethink organization theory. Logics of Organization Theory sets forth and applies a new language for theory building based on a nonmonotonic logic and fuzzy set theory. In doing so, not only does it mark a major advance in organizational theory, but it also draws lessons for theory building elsewhere in the social sciences. Organizational research typically analyzes organizations in categories such as "bank," "hospital," or "university." These categories have been treated as crisp analytical constructs designed by researchers. But sociologists increasingly view categories as constructed by audiences. This book builds on cognitive psychology and anthropology to develop an audience-based ...

Deontic conflicts pose an important challenge to deontic logicians. The standard account —standard deontic logic, SDL— is not apt for addressing this challenge since it trivializes conflicts. Two main stratagems for gaining conflict-tolerance have been proposed: to weaken SDL in various ways, and to contextualize the reign of SDL to consistent subsets of the premise set. The latter began with the work of van Fraassen and has been further developed by Horty. In this paper we characterize this second ap- proach in general terms. We also study three basic ways to contextualize SDL and supplement each of these with a dynamic proof theory in the framework of adaptive logics.

The capability of drawing defeasible conclusions in presence of partial information is a crucial factor of intelligent behavior. To achieve this capability, human beings resort to a particular kind of knowledge, called default knowledge. The most significant property of default knowledge is that it can be exploited in the reasoning process even if there is only partial information about the satisfaction of the preconditions which allow its application, on condition that there is no reason to believe that such preconditions are not satisfied. If new information becomes available from which the falsity of such preconditions can be deduced, the conclusions derived from the application of default knowledge have to be retracted. This particular form of reasoning, involving the use of default knowledge, may be called defeasible reasoning. In order to build automated reasoning systems including defeasible reasoning capabilities, many extensions of classical logic have been proposed as mode...

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed-world reasoning of particular interest for human cognition. Byrne's "suppression" data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine-grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3-valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning.

This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics. We define a nonmonotonic logic, called equilibrium logic, based on the least constructive extension, N2, of the intermediate logic of “here-and-there”. We show that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz. We thereby obtain a very simple characterisation of answer set semantics as a form of minimal model reasoning in N2, while equilibrium logic itself provides a natural generalisation of this semantics to arbitrary theories. We discuss briefly some consequences and applications of this result.

Building theories of organizations is challenging: theories are partial and "folk" categories are fuzzy. The commonly used tools--first-order logic and its foundational set theory--are ill-suited for handling these complications. Here, three leading authorities rethink organization theory. Logics of Organization Theory sets forth and applies a new language for theory building based on a nonmonotonic logic and fuzzy set theory. In doing so, not only does it mark a major advance in organizational theory, but it also draws lessons for theory building elsewhere in the social sciences. Organizational research typically analyzes organizations in categories such as "bank," "hospital," or "university." These categories have been treated as crisp analytical constructs designed by researchers. But sociologists increasingly view categories as constructed by audiences. This book builds on cognitive psychology and anthropology to develop an audience-based ...

We study a bimodal nonmonotonic logic MBNF suggested in (Lifschitz, 1994) as a generalization of a number of nonmonotonic formalisms We show first that it is equivalent to a certain non- modal system involving rules of a special kind Next, it is shown that the latter admits a modal representation that uses only one modal opera tor the operator of

This paper introduces a novel logical framework for concept-learning called brave induction. Brave induction uses brave inference for induction and is useful for learning from incomplete information. Brave induction is weaker than explanatory induction which is normally used in inductive logic programming, and is stronger than learning from satisfiability, a general setting of concept-learning in clausal logic. We first investigate

This paper provides a logical framework for comparing inductive capabilities among agents having different background theories. A background theory is called inductively equivalent to another background theory if the two theories induce the same hypotheses for any observation. Conditions of inductive equivalence change depending on the logic of representation languages and the logic of induction or inductive logic programming (ILP).