A Groebner Bases Based Many-Valued Modal Logic Implementation in Maple

The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.

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A new approach to the logic of discovery

Theoria Beograd ◽

10.2298/theo0701007m ◽

2007 ◽

Vol 50 (1) ◽

pp. 7-27

Author(s):

Gerald Massey

Keyword(s):

Modal Logic ◽

Scientific Discovery ◽

Traditional View ◽

New Approach ◽

Logic Of Discovery ◽

Good Fortune ◽

High Incidence ◽

History Of ◽

Deep Sense

Contending that the quest for a logic of scientific discovery was prematurely abandoned, the author lays down eight phenomena that such a logic or theory must explain: the banality of scientific discovery; the trainability of scientists; the high incidence of simultaneous discoveries; the ubiquity of relative novices; the fact of scientific genius; the barrenness of isolated workers; the incommensurability of concepts of successive theories; and the quasi-incorporation of old concepts, objects, and methods in successor theories, The author then presents a new theory or logic of discovery according to which discoveries are the termini of "tweak paths" generated when scientists "tinker" with the laws, concepts, methods, and instruments of a given theory. Tinkering and tweaking are illustrated by examples from many-valued and modal logic and from Darwinian biology. Through the history of planetary discovery, the accidental role played by luck or good fortune in some discoveries is explored, but the author emphasizes that in a deep sense serendipity is an in eliminable feature of all scientific discovery because scientists never know m advance whether their tweaks will lead to dead ends or to positive developments. The author's new theory of scientific discovery is shown to account for all eight explananda, ft also reveals science to be a more egalitarian enterprise than the traditional view of scientific discovery as ultimately inexplicable depicts it.

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Implications for the epistemic auxiliaries

10.1093/oso/9780198701347.003.0006 ◽

2017 ◽

Author(s):

Daniel Lassiter

Keyword(s):

Modal Logic ◽

Probabilistic Theory ◽

Context Sensitive ◽

Rule Out

The semantics of the adjectives places strong constraints on theories of the better-studied epistemic auxiliaries. This chapter motivates some basic connections – for instance, must asymmetrically entails likely; likely asymmetrically entails might and possible; and certain asymmetrically entails must (modulo the evidential presupposition of the latter). In addition, I present a lottery experiment showing that might has a context-sensitive meaning that is stronger than possible’s. These connections suffice to rule out the classical treatment from modal logic, as revived recently by von Fintel & Gillies (2010). It also rules out Kratzer’s (1991) theory. The probabilistic theory of Swanson (2006); Lassiter (2011, 2016) satisfies our desiderata, though, as does Swanson’s (2015) blend of the scalar semantics with Kratzer’s account. Both have access to a plausible formalization of must’s evidential component, but the latter has additional interesting features – both strengths and weaknesses – involving dualities and the treatment of so-called “epistemic ought”.

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Necessary Existence

10.1093/oso/9780198746898.001.0001 ◽

2018 ◽

Cited By ~ 2

Author(s):

Alexander R. Pruss ◽

Joshua L. Rasmussen

Keyword(s):

Modal Logic ◽

Abstract Objects ◽

Classical Theism ◽

Necessary Being ◽

Necessary Existence ◽

Concrete Entity ◽

The Universe

A necessary being is a concrete entity that cannot fail to exist. An example of such a being might be the God of classical theism or the universe of necessitarians. Necessary Existence offers and carefully defends a number of novel arguments for the thesis that there exists at least one necessary being, while inviting the reader to a future investigation of what the neccessary being(s) is (are) like. The arguments include a defense of a classic contingency argument, a series of new modal arguments from possible causes, an argument from abstract objects, and a Gödelian argument from perfections. Furthermore, arguments against the possibility of a necessary being are critically examined. Among these arguments are old and new arguments from conceivability, a subtraction argument, problems with causation, and an argument from parsimony. Necessary Existence also includes a defense of the axioms of S5 modal logic, which is a framework for understanding several arguments for necessary existents.

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More on Modal Aspects of Default Logic1

Fundamenta Informaticae ◽

10.3233/fi-1992-171-207 ◽

1992 ◽

Vol 17 (1-2) ◽

pp. 99-116

Author(s):

V. Wiktor Marek ◽

Miroslaw Truszczynski

Keyword(s):

Modal Logic ◽

Default Logic ◽

Nonmonotonic Logic ◽

Default Reasoning ◽

Default Theory ◽

Autoepistemic Logic ◽

The Relationship ◽

Natural Classes ◽

Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

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