Heinrich Wansing

This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics. The authors cover themes such as the knowability paradox, tableaux and sequent calculi, natural deduction, definite descriptions, identity, truth, dialetheism and possible worlds semantics. The developments presented here focus on challenging problems in the specification of fundamental philosophical notions, as well as presenting new techniques and tools, thereby contributing to the development of the field. Each chapter contains a bibliography, to assist the reader in making connections in the specific areas covered. Thus this work provides both a starting point for further investigations into philosophical logic and an update on advances, techniques and applications in a dynamic field. The chapters originate from papers presented during the Trends in Logic XI conference at the Ruhr University Bochum, June 2012.

ABSTRACT We consider certain objections against Fagin's and Halpern's logic of general awareness and interpret them as doubts whether there exists a correspondence theory for awareness logic with respect to sieve models. We present a non-compositional translation from epistemic formulas into first-order logic as the essential ingredient of such a correspondence theory and define a suitable notion of bisimulation. Moreover, in order to further underline the power of sieve models, we prove the Lewis system SI to be complete for a relational interpretation which is equivalent to the sieve model semantics.

A prominent issue in mainstream epistemology is the controversy about doxastic obligations and doxastic voluntarism. In the present paper it is argued that this discussion can benefit from forging links with formal epistemology, namely the combined modal logic of belief, agency, and obligation. A stit-theory-based semantics for deontic doxastic logic is suggested, and it is claimed that this is helpful and illuminating in dealing with the mentioned intricate and important problems from mainstream epistemology. Moreover, it is argued that this linking is of mutual benefit. The discussion of doxastic voluntarism directs the attention of doxastic logicians to the notion of belief formation and thus to dynamic aspects of beliefs that have hitherto been neglected. The development of a formal language and semantics for ascriptions of belief formation may contribute to clarifying the contents and the implications of voluntaristic claims. A simple observation concerning other-agent nestings of stit-operators, for instance, may help illuminating the notions of making belief and responsibility for beliefs of others. In this way, stit-theory may serve as a bridge between mainstream and formal epistemology.