On an Axiomatic System of Modal Logic

1968 ◽  
Vol 14 (1-5) ◽  
pp. 61-66
Author(s):  
Akira Nakamura
Keyword(s):  
Modal Logic ◽  
Axiomatic System

An infinitary axiomatization of dynamic topological logic

2020 ◽  
Author(s):  
Somayeh Chopoghloo ◽  
Morteza Moniri
Keyword(s):  
Continuous Function ◽  
Modal Logic ◽  
Topological Space ◽  
Axiomatic System ◽  
Proof System ◽  
Strong Completeness ◽  
Alexandrov Spaces ◽  
Modal Language ◽  
Derivation Rule ◽  
Dynamic Topological Logic

Abstract Dynamic topological logic ($\textsf{DTL}$) is a multi-modal logic that was introduced for reasoning about dynamic topological systems, i.e. structures of the form $\langle{\mathfrak{X}, f}\rangle $, where $\mathfrak{X}$ is a topological space and $f$ is a continuous function on it. The problem of finding a complete and natural axiomatization for this logic in the original tri-modal language has been open for more than one decade. In this paper, we give a natural axiomatization of $\textsf{DTL}$ and prove its strong completeness with respect to the class of all dynamic topological systems. Our proof system is infinitary in the sense that it contains an infinitary derivation rule with countably many premises and one conclusion. It should be remarked that $\textsf{DTL}$ is semantically non-compact, so no finitary proof system for this logic could be strongly complete. Moreover, we provide an infinitary axiomatic system for the logic ${\textsf{DTL}}_{\mathcal{A}}$, i.e. the $\textsf{DTL}$ of Alexandrov spaces, and show that it is strongly complete with respect to the class of all dynamical systems based on Alexandrov spaces.

Modal Logic

1980 ◽  
Author(s):  
Brian F. Chellas
Keyword(s):  
Modal Logic

Modality and folk psychology

2019 ◽  
Vol 28 (1) ◽  
pp. 19-27
Author(s):  
Ja. O. Petik
Keyword(s):  
Modal Logic ◽  
Brain Activity ◽  
Formal System ◽  
Philosophy Of Logic ◽  
Psychological States ◽  
Formal Systems ◽  
Modern Psychology ◽  
Philosophical Interpretation ◽  
Important Direction

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.

Hilbert-style proof Calculus for Propositional Logic in ABC notation

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Propositional Logic ◽  
Inference Rule ◽  
Modus Ponens ◽  
Axiomatic System ◽  
First Contact

All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

A new approach to the logic of discovery

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.

Implications for the epistemic auxiliaries

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”.

Necessary Existence

2018 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document