Trends In Logic

Download or read book Protoalgebraic Logics written by Janusz Czelakowski and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is to present recent ideas in logic centered around the notion of a consequence operation. We wish to show these ideas in a factually and materially connected way, i.e., in the form of a consistent theory derived from several simple assumptions and definitions. These ideas have arisen in many research centers. The thorough study of their history can certainly be an exciting task for the historian of logic; in the book this aspect of the theory is being played down. The book belongs to abstract algebraic logic, the area of research that explores to a large extent interconnections between algebra and logic. The results presented here concern logics defined in zero-order languages (Le., quantifier-free sentential languages without predicate symbols). The reach of the theory expounded in the book is, in fact, much wider. The theory is also valid for logics defined in languages of higer orders. The problem of transferring the theory to the level of first-order languages has been satisfactorily solved and new ideas within this area have been put forward in the work of Blok and Pigozzi [1989].

Download or read book Trends in Logic written by Vincent F. Hendricks and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.

Download or read book Logic in High Definition written by Alessandro Giordani and published by Springer Nature. This book was released on 2020-11-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume clusters together issues centered upon the variety of types of intensional semantics. Consisting of 10 contributions, the volume is based on papers presented at the Trends in Logic 2019 conference. The various chapters introduce readers to the topic, or apply new types of logical semantics to elucidate subtleties of logical systems and natural language semantics. The book introduces hyperintentional systems that aim at solving some open philosophical problems. Specifically, the first three studies focus on relating semantics, while the following ones discuss fundamental issues related to hyper-intensional semantics or develop hyper-intensional frameworks to address issues in modal, epistemic, deontic and action logic. Authors in this volume present original results on logical systems but also extend beyond this by offering philosophical considerations on the topic as well. This volume will appeal to students and researchers in the field of logic.

Download or read book Types, Tableaus, and Gödel’s God written by M. Fitting and published by Springer Science & Business Media. This book was released on 2002-05-31 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Parts of the book are mathematical, parts philosophical.

Download or read book Anaphora and Type Logical Grammar written by Gerhard Jäger and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Type Logical Grammar is a framework that emerged from the synthesis of two traditions: Categorial Grammar from formal linguistics and substructural logics from logic. Grammatical composition is conceived as resource conscious logical deduction. Such a grammar is necessarily surface oriented and lexicalistic. The Curry-Howard correspondence supplies an elegant compositional mapping from syntax to semantics. Anaphora does not seem to fit well into this framework. In type logical deductions, each resource is used exactly once. Anaphora, however, is a phenomenon where semantic resources are used more than once. Generally admitting the multiple use of lexical resources is not possible because it would lead to empirical inadequacy and computational intractability. This book develops a hybrid architecture that allows to incorporate anaphora resolution into grammatical deduction while avoiding these consequences. To this end, the grammar logic is enriched with a connective that specifically deals with anaphora. After giving a self-contained introduction into Type Logical Grammar in general, the book discusses the formal properties of this connective. In the sequel, Jäger applies this machinery to numerous linguistic phenomena pertaining to the interaction of pronominal anaphora, VP ellipsis and quantification. In the final chapter, the framework is extended to indefiniteness, specificity and sluicing.

Download or read book Dynamic Logic. New Trends and Applications written by Manuel A. Martins and published by Springer Nature. This book was released on 2020-12-21 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the Third International Workshop on Dynamic Logic, DaLí 2019, held in Prague, Czech Republic in October 2020. Due to COVID-19 the workshop has been held online. The 17 full papers presented together with 6 short papers were carefully reviewed and selected from 31 submissions. The theoretical relevance and practical potential of dynamic logic is a topic of interest in a number of scientific venues, from wide-scope software engineering conferences to modal logic specific events. The DaLí 2020 workshop is exclusively dedicated to Dynamic logic and aims at filling this gap and creating a heterogeneous community of colleagues, from Academia to Industry, from Mathematics to Computer Science.

Download or read book Methods of Cut-Elimination written by Matthias Baaz and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on cut-elimination in first-order predicate logic from an algorithmic point of view. Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs). The first part investigates traditional reductive methods from the point of view of proof rewriting. Within this general framework, generalizations of Gentzen's and Sch\”utte-Tait's cut-elimination methods are defined and shown terminating with ACNFs of the original proof. Moreover, a complexity theoretic comparison of Gentzen's and Tait's methods is given. The core of the book centers around the cut-elimination method CERES (cut elimination by resolution) developed by the authors. CERES is based on the resolution calculus and radically differs from the reductive cut-elimination methods. The book shows that CERES asymptotically outperforms all reductive methods based on Gentzen's cut-reduction rules. It obtains this result by heavy use of subsumption theorems in clause logic. Moreover, several applications of CERES are given (to interpolation, complexity analysis of cut-elimination, generalization of proofs, and to the analysis of real mathematical proofs). Lastly, the book demonstrates that CERES can be extended to nonclassical logics, in particular to finitely-valued logics and to G\"odel logic.