We extend meet-combination of logics for capturing the consequences that are common to both logics. With this purpose in mind we define meet-combination of consequence systems. This notion has the advantage of accommodating different ways of presenting the semantics and the deductive calculi. We consider consequence systems generated by a matrix semantics and consequence systems generated by Hilbert calculi. The meet-combination of consequence systems generated by matrix semantics is the consequence system generated by their product. On the other hand, the (...) meet-combination of consequence systems generated by Hilbert calculi is the consequence system generated by their interconnection. We investigate preservation of several properties. Capitalizing on these results we show that interconnection provides an axiomatization for the product. Illustrations are given for intuitionistic and modal logics, Łukasiewicz logic and some paraconsistent logics. (shrink)

In a recent article in this journal, Calemi challenges the Küng-Armstrong trilemma, a well-known objection to traditional class nominalism, by proposing a fusion of class nominalism with Zermelo-Fraenkel set theory (ZF). In this note, we argue that ZF-class nominalism faces significant challenges in the form of incompleteness and potential paradoxes stemming from Gödel’s incompleteness theorem. We will explore these issues in detail, highlighting the key implications for the viability of ZF-class nominalism as a philosophical position.

This paper outlines three broad ways one might think about logical correctness: the Realist approach, the One-Language approach and my own Neo-Carnapian view. Although the realist and one-language views have dominated the philosophy of logic in recent years, I argue against them, favouring of the Neo-Carnapian approach.

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E  the rule of restricted assertion or equivalently Ackermann’s δ-rule  is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics (...) for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of the ternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction ◦ – as well as the converse conditional ←. (shrink)

In this paper, we consider how an agent may manage a questioning agenda in a situation where multiple information sources are available. We work within the framework of formal dialogue systems with the underpinning of Inferential Erotetic Logic. Firstly, we present the formal dialogue system DL(IEL)mult for managing multi-agent information retrieval. Then, we extend the proposed system so that it is capable of representing group and individual levels for the question decomposition process. We also propose two measures for evaluating information (...) sources: their cooperativeness and success levels; next, we analyse how the choice of agents may influence the way in which a solution for a given problem is reached. (shrink)