College Publications logo   College Publications title  
View Basket
Homepage Contact page
Cadernos de Lógica e Computação
Cadernos de Lógica e Filosofia
Cahiers de Logique et d'Epistemologie
Communication, Mind and Language
Cuadernos de lógica, Epistemología y Lenguaje
Encyclopaedia of Logic
IfColog series in Computational Logic
Journal of Applied Logics - IfCoLoG Journal of Logics and their Applications
Law and Society
Logic PhDs
Logic, Methodology and Philosophy of Science
The Logica Yearbook
Neural Computing and Artificial Intelligence
The SILFS series
Studies in Logic
History of Logic
Logic and cognitive systems
Mathematical logic and foundations
Studies in Logic and Argumentation
Studies in Talmudic Logic
Texts in Mathematics
Digital Downloads
Information for authors
About us
Search for Books

Studies in Logic


Fathoming Formal Logic: Vol II

Semantics and Proof Theory for Predicate Logic

Odysseus Makridis

This text, volume II of a two-volume work, examines in depth the so-called “standard” predicate logic. Including a foundational lexicon of terms and a detour through the classical propositional logic, this volume can be used independently of the first.

As a means toward teasing out theoretical subtleties and negotiating formal and philosophic challenges, this work uses detailed examples and exercises; because of this feature, the text can also be used to study formal logic in a rigorous fashion.

Given its expressive power, predicate logic is deemed as minimally adequate for formalization of such fundamental languages as that of Mathematics and for translations of the meanings of English (or other natural-language) sentences. Laying foundations in this area is key to a technical understanding of deductive reasoning and to honing rigorous critical thinking and problem-solving skills.
Notable (some of them unusual) features that are covered in the present volume include the following:

The overview of propositional logic includes positive semantic trees, in addition to the negative semantic tree method.
Prenex forms and conversion to equivalent prenex forms.
Relational (ultimately polyadic) predicate symbols, function symbols and identity are made available.
The decision problem and the Lӧwenheim Result are discussed.
Proof-theoretic methods are presented analytically and extensive justifications are offered for the required restrictions on the deduction rules.
The semantics of predicate logic modeling are presented in analytical detail along with inquiries into the logical-philosophical significance of predicate logic.
Translation from English into the predicate logic idiom (formalization, symbolization) is examined thoroughly, accompanied by motivating linguistic observations and thorough scrutiny of available options; aspects of this inquiry include translations under restricted and unrestricted domains, translations of compacted predicates, rendering of non-classically quantified phrases, translations of numerical statements, definite descriptions and regimentation, and guidance on how to render existential presuppositions.
Disambiguation is imposed on translations and an extensive list of examples is presented.
Translations of idiomatic linguistic expressions are studied.
Semantic tree decision procedures (for finitarian domains) – including negative and positive semantic tree systems – are constructed and applied.
Appendices on Set Theory, Mathematical Induction and Dialogical Logic are presented.

1 February 2018


© 2005–2018 College Publications / VFH webmaster