Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas with the notion of structured families of labelled formulas with algebraic structures. This approach has far reaching consequences for the methodology of logics and their semantics, and the book studies the main features of such systems along with their applications. It will interest logicians, computer scientists, philosophers and linguists.

Causal reasoning has become very important in the last few years in logic based action theories. In this article, we study how causal inference has been integrated and used in action theories. After presenting and discussing criteria considered as the most meaningful, we present four formalisms which are approaches to actions and causality and we try to situate each formalism in relation to the criteria.

A sequent calculus of a new sort is extracted from the Prolog program leanTAP. This calculus is sound and complete, even though it lacks almost all structural rules. Thinking of leanTAP as a sequent calculus provides a new perspective on it and, in some ways, makes it easier to understand. It is also easier to verify correctness and completeness of the Prolog implementation. In addition, it suggests extensions to other logics, some of which are considered here.

This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...

Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book (...) can also be used as an introduction to these logical systems form a procedural perspective. Readership: Computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory. (shrink)

The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only to (...) establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics. (shrink)

In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl''s ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors'' Triviality Result.

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.

In this paper we (Laura Giordano, Nicola Olivetti and myself) propose a conditional logic to represent iterated belief revision systems. We propose a set of postulates for belief revision which are a small variant of Darwiche and Pearl's ones.The resulting conditional logic has a standard semantics in terms of selection function models, and provides a natural representation of epistemic states. A Representation Theorem establishes a correspondence between iterated belief revision systems and conditional models. Our Representation Theorem does not entail Gärdenfors' (...) Triviality Result. (shrink)