Natural Deduction Hybrid Systems And Modal Logics
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Natural Deduction, Hybrid Systems and Modal Logics
Author: Andrzej Indrzejczak
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-07-03
A good title should be informative enough to illuminate a potential reader on the content of a book. We hope that the present title gives at least some hints of what this book is about. The notion of natural deduction or modal logic are rather well known, but the notion of “hybrid system” certainly needs some explanation. In short, this study may be seen as a kind of search for good deductive systems. We think of systems good in practice which may be applied with easenotonlybywelltrainedlogiciansbutalso, forexample, byphilosophers who need handy deductive tools accompanying their analyses. In parti- lar, we are interested in providing systems that may be widely applied in teaching logic. Nowadays one may observe that several courses in “critical thinking” tend to eliminate courses in practical logic. On the other hand, logic is often taught as a strictly mathematical discipline in very dema- ing courses. It is important to ?ll the gap between these extrema, and the crucial ingredient of any course which is supposed to teach how to use logic, is certainly a suitable deductive system. Since we address this work to a wide audience interested in applications of logic, we were trying to make it self-contained and accessible to a reader with no hard training in logic. The assumed reader should have some ba- ground in logic (an elementary course covering classical propositional and ?rst-order logic with basics of set theory is enough) but not necessarily in modal logic.
Natural Deduction, Hybrid Systems and Modal Logics
Here is an extensive treatment of Natural Deduction and related proof systems, focused on practical aspects of proof methods. Necessary background material is provided, including a presentation of Modal Logics, First-Order Modal and Hybrid Modal Logics.
Hybrid Logic and its Proof-Theory
Author: Torben Braüner
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-11-17
This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).