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.

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.

PCCP is the much discussed claim that the probability of a conditional A → B is conditional probability. Triviality results purport to show that PCCP – as a general claim – is false. A particularly interesting proof has been presented in (Hájek, 2011), who shows that – even if a probability distribution P initially satisfied PCCP – a rational update can produce a non-PCCP probability distribution. We argue that the notion of rational update in this argumentation is construed in much too broad a way. In order to make the argumentation precise, we discuss the general rules for modeling conditionals in probability spaces and present formalized version(s) of PCCP and of minimal assumptions concerning the appropriate spaces. Using the introduced apparatus we give a detailed analysis of Hájek’s (2011) triviality proof and show that it is based on an application of revision rules which allow one to construct probability distributions violating not only PCCP, but also fundamental properties of conditionals. This means that they do not really provide arguments against PCCP, properly formalized. We also discuss a Dutch Book argument which shows that the updated belief system is not coherent. This gives an additional, strong argument against accepting the update rules. We also discuss the Converse Dutch Book theorem and argue, that even if the produced probability measure seems to violate it, it cannot serve as the counterexample, as it is not an appropriate model for conditionals. Ultimately, we show that important arguments against PCCP fail.

I presented a sub-classical relating logic based on a relating via an NL-inspired relating relation Rcss. The relation Rcss is motivated by the NL-phenomenon of phrasal (subsentential) coordination, exhibiting an important aspect of contents relating among the arguments of binary connectives. The resulting logic Lcss can be viewed as a relevance logic exhibiting a contents related relevance, stronger than the variable-sharing property of other relevance logics like R. Note that relating here is not “tailored” to justify some predetermined logic; rather, the relating relation is independently justified, and induces a logic not previously investigated.

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.

I argue that the Stoic logic is explosive. The claim applies to the Stoics' syllogistic in the strictest sense, because there is a provable syllogism which qualifies as a principle of explosion. It applies also to the general consequence operation, in the sense that every sentence is derivable from any pair containing both a sentence and the negation of the sentence. Finally, it applies to the connective of implication (conditional), in the sense that any conditional is derivable, providing its antecedent is a conjunction of a sentence and the negation of the sentence. All three claims allow weakening, i.e., additions of extra premises to an inference or extra conjuncts to the antecedent of an implication, respectively. Consequently, no concept of relevance, let alone paraconsistency or connexivity is applicable to the Stoic logic; in particular, the Stoics' connective of implication is either material (Boolean) or formal (strict).

Accounting for the epistemic contribution of deduction has been a pervasive problem for logicians interested in deduction, such as, among others, Jakko Hintikka. The problem arises because the conclusion validly deduced from a set of premises is said to be “contained” in that set; because of this containment relation, the conclusion would be known from the moment the premises are known. Assuming this, it is problematic to explain how we can gain knowledge by deducing a logical consequence implied by a set of known premises. To address this problem, we offer an alternative account of the epistemic contribution of deduction as the process required to deduce a conclusion or a theorem, understanding such a process not only in terms of the number of steps in the derivation but also, more importantly, in terms of the reason for or justification for every step. That is, we do not know a proposition unless we have a justification or proof of that proposition. With this goal in mind, we develop a justification logic system which exhibits the epistemic contribution of a deductive derivation as the resulting justified formula.

This paper introduces two languages and associated logics designed to afford perspicuous representations of a range of natural language arguments involving adverbs and the like: first-order logic with basic adverbs (FOL-BA) and first-order logic with scoped adverbs (FOL-SA). The guiding logical idea is that an adverb can come between a term and the rest of the statement it is a part of, resulting in a logically stronger statement. I explain various interesting challenges that arise in the attempt to implement the guiding idea, and provide solutions for some but not all of them. I conclude by outlining some directions for further research.

The article proposes a formal semantics of happiness and sadness modalities in the imperfect information setting. It shows that these modalities are not definable through each other and gives a sound and complete axiomatization of their properties.

There are many approaches to paraconsistency, ranging from the very moderate to the more radical. In this paper I explore and extend the more radical end of the spectrum, where there are truth-value gluts. In particular I will look at paraconsistent metatheory – the machinery of truth, validity, and proof  as developed in a glut-friendly paraconsistent setting. The aim is to evaluate the philosophical and technical tenability of such an approach. I will show that there are very significant technical challenges to face on this sort of radical approach, but that there is good philosophical support for facing these challenges.