Books by 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 L¿wenheim 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.

This text, volume I of a two-volume work, examines in depth the standard (also called classical) propositional logic. This is a theoretical work that aims at a philosophically exploratory and technically rigorous presentation. Detailed examples and exercises are used to tease out technical minutiae, solidify understanding, and point to logical-philosophical puzzles and challenges; because of this feature, the text can also be used to study formal logic in a rigorous fashion. The study of propositional logic can reward the dedicated and patient student by unveiling technical mysteries of critical thinking and problem-solving, by shedding light on relevant concepts in the study of reasoning, by showing how the powerful formal tools and methods work in applications, and by unlocking the crypts of logical analysis. It can hone insights that further contribute both to understanding how logic works and to preparing for future pursuits in the study of formal reasoning.This text encompasses certain topics and decision mechanisms that are usually absent from Logic texts and can be canvassed only through acquaintance with ever larger chunks of the extant bibliography. Rarely covered topics of the present text include: possible-worlds analysis, analyticity and non-cognitivism, detailed investigations of logical relations, alternative grammatical and computational systems, truth tables for dynamic flow of information and corrected truth tables, negative and positive semantic trees, normal forms and Karnaugh maps, Intuitionistic natural deduction, normalization and harmony in proof-theoretic systems, and dialogical logic.