The main object of this paper is to provide the logical machinery needed for a viable basis for talking of the 'consequences', the 'content', or of 'equivalences' between inconsistent sets of premisses.With reference to its maximal consistent subsets (m.c.s.), two kinds of'consequences' of a propositional set S are defined. A proposition P is a weak consequence (W-consequence) of S if it is a logical consequence of at least one m.c.s, of S, and P is an inevitable consequence (/-consequence) of S if it is a logical consequence of all the m.c.s. of S. The set of W-consequences of a set S it determines (up to logical equivalence) its m.c.s. (This enables us to define a normal form for every set such that any two sets having the same W-consequences have the same normal form.) The W-consequences and/-consequences will not do to define the 'content' of a set S. The first is too broad, may include propositions mutually inconsistent, the second is too narrow. A via media between these concepts is accordingly defined: P is a P-consequence of S, where P is some preference criterion yielding some of the m.c.s, of S as preferred to others, and P is a consequence of all of the P-preferred m.c.s, of S. The bulk of the paper is devoted to discussion of various preference criteria, and also surveys the application of this machinery in diverse contexts -for example, in connection with the processing of mutually inconsistent reports.

This paper is concerned with answers to questions and their relations to assertions. Since in asserting a proposition the speaker is answering a question and in asking a question he expresses his commitment to the truth of its presupposition, it is argued that both acts of asking and of asserting are representable in terms of sets of question-answer pairs. A formal language is described for these pairs. The first argument, the question, is an open formula in a fully typed language containing the usual sentential connectives. The second argument, a categorial answer, is a term of the appropriate type. Terms of the same type may be combined with term-connectives, and quantification over open pairs yield (complex) terms. Semantically, these terms yield three kinds of categorial answers to a given question: Direct answers denote elements of the domain of the appropriate category; diminutive answers denote a subset of this domain, within which a direct answer is to be found. If the subset is the domain itself, then the pair represents the presupposition of the question that it has a true answer within the domain; Corrective answers consist in the (term-) negation of the presupposition. Quantification and description are introduced only by quantification over terms, yielding, in effect, Aristotelian quantification. This approach enables us to distinguish sentential connectives from term connectives, and to distinguish between different contrastive foci of sentence tokens of the same sentence type. Moreover, we are able to define the semantic presupposition of both indicative and interrogative sentences in terms of the presupposition of a question that it has a true answer. Finally, we are able to define a natural concept of semantic relevance of one utterance to another in terms of the question-answer relation, accounting for both the local relevance of a discussion, in which each utterance is semantically relevant to the preceding utterance although the subject of the discussion may shift, and for the global relevance of a discussion where two utterances may seem locally irrelevant to each other, though they are so related by being both somehow relevant to the problem under discussion.The formal discussion was written in Gent, Belgium, with the support of the Belgian Government through the Ministry of National Education and Dutch Culture. Some of the better ideas were developed during the discussions I had with Diderik Batens.

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A speech is an ordered set of speech-acts normally used to express commitments to propositions, which a speaker S performs in some context. Employing the point of view of the audience and by using the formal language CA V for conditional assertion, a concept of pragmatical presuppositions and the order of the speech-acts performed, we determine at each step to which possible propositions S expressed his commitment both at this step and so far in the speech. We distinguish different cases where S expresses commitments inconsistent with his previous commitments. S may do so, to some extent, and change his mind, while in other cases this will cause the logical end of the speech.

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