Trends in Logic

2 primary works

Protoalgebraic Logics

by Janusz Czelakowski

Published 30 April 2001

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].

Freedom and Enforcement in Action

by Janusz Czelakowski

Published 25 June 2015

Action theory is the object of growing attention in a variety of scientific disciplines and this is the first volume to offer a synthetic view of the range of approaches possible in the topic. The volume focuses on the nexus of formal action theory with a startlingly diverse set of subjects, which range from logic, linguistics, artificial intelligence and automata theory to jurisprudence, deontology and economics. It covers semantic, mathematical and logical aspects of action, showing how the problem of action breaks the boundaries of traditional branches of logic located in syntactics and semantics and now lies on lies on the borderline between logical pragmatics and praxeology.

The chapters here focus on specialized tasks in formal action theory, beginning with a thorough description and formalization of the language of action and moving through material on the differing models of action theory to focus on probabilistic models, the relations of formal action theory to deontic logic and its key applications in algorithmic and programming theory. The coverage thus fills a notable lacuna in the literary corpus and offers solid formal underpinning in cognitive science by approaching the problem of cognition as a composite action of mind.