This open access book makes a case for extending logic beyond its traditional boundaries, to encompass not only statements but also also questions. The motivations for this extension are examined in ...detail. It is shown that important notions, including logical answerhood and dependency, emerge as facets of the fundamental notion of entailment once logic is extended to questions, and can therefore be treated with the logician’s toolkit, including model-theoretic constructions and proof systems. After motivating the enterprise, the book describes how classical propositional and predicate logic can be made inquisitive—i.e., extended conservatively with questions—and what the resulting logics look like in terms of meta-theoretic properties and proof systems. Finally, the book discusses the tight connections between inquisitive logic and dependence logic.
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the ...properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His ...philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.
Infotext (nur auf Basis des Vorgängers): This two-volume set of LNAI 14739-14740 constitute the proceedings of the 12th International Joint Conference on Automated Reasoning, IJCAR 2024, held in ...Nancy, France, during July 3-6, 2024. The 39 full research papers and 6 short papers presented in this book were carefully reviewed and selected from 115 submissions. The papers focus on the following topics: theorem proving and tools; SAT, SMT and Quantifier Elimination; Intuitionistic Logics and Modal Logics; Calculi, Proof Theory and Decision Procedures; and Unification, Rewriting and Computational Models. This book is open access.
This two-volume set of LNAI 14739-14740 constitute the proceedings of the 12th International Joint Conference on Automated Reasoning, IJCAR 2024, held in Nancy, France, during July 3-6, 2024. The 39 ...full research papers and 6 short papers presented in this book were carefully reviewed and selected from 115 submissions. The papers focus on the following topics: theorem proving and tools; SAT, SMT and Quantifier Elimination; Intuitionistic Logics and Modal Logics; Calculi, Proof Theory and Decision Procedures; and Unification, Rewriting and Computational Models. This book is open access.
(L\)-Modules Saidi Goraghani, Simin; Borzooei, Rajab Ali
Bulletin of the Section of Logic,
2024, Letnik:
53, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper, considering \(L\)-algebras, which include a significant number of other algebraic structures, we present a definition of modules on \(L\)-algebras (\(L\)-modules). Then we provide some ...examples and obtain some results on \(L\)-modules. Also, we present definitions of prime ideals of \(L\)-algebras and \(L\)-submodules (prime \(L\)-submodules) of \(L\)-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime \(L\)-submodules.
Jakowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jakowski's idea to define his discussive ...logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2P.
CORE TYPE THEORY Abstract van Dijk, Emma; Ripley, David; Gutierrez, Julian
Bulletin of the Section of Logic,
01/2023, Letnik:
52, Številka:
2
Journal Article
Recenzirano
Neil Tennant's core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to ...bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant's own, but it is very closely related. The difference matters for our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant's proof system for core logic is not strongly normalizing, our modified system is.
