Ole Thomassen Hjortland

Speech Acts, Categoricity, and the Meanings of Logical Connectives

In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulae. Such systems lend themselves to an inferentialist story about how truth-conditional content of connectives can be determined by inference rules. In particular, for classical logic there is a bilateral proof system which has a property that Carnap (1943) called categoricity. We show that categorical systems can be given for any finite many-valued logic using n-sided sequent calculus. These systems are understood as a further development of bilateralism—call it multilateralism. The overarching idea is that multilateral proof systems can incorporate the logic of a variety of denial speech acts. So against Frege we say that denial is not the negation of assertion, and with Mark Twain, that denial is more than a river in Egypt.

Dynamic consequence for soft information

This article looks at so-called dynamic consequence relations for models of soft information change. We provide a sound, complete calculus for one-step soft dynamic consequence relations. We then study a generalization to sequences of updates, for which we show a number of valid and invalid structural rules.

Theories of truth and the maxim of minimal mutilation

Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.

Special issue on substructural logic and information dynamics: introduction

This special issue arose out of two workshops held in Prague and Munich in 2011 and 2013.1 It puts together a number of contributions combining substructrual logic (SL) and dynamic epistemic logic (DEL) in order to address, first, the problem of logical omniscience [10], secondly, the question of interpreting the Routley–Meyer semantics for substructural logic [5], and finally, the challenge of providing a proof theory that enjoys normalization or cut-elimination for DEL [9]. This issue is of course not the first encounter between substructural logic and logical models of information dynamics, but it shows that their relationship is much more than a one-night stand. On the one hand, substructural systems have been extensively used to tackle the logical omniscience problem, in both classical, static epistemic logic and in its dynamic extensions [6]. The first two contributions of this issue are by key contributors in this tradition. Sedlár’s paper opens by providing a very general substructural framework for modelling knowledge, its dynamics and its relation to non-mononotic reasoning. Bílkova et al. follow a similar thread, this time generalizing previous work of theirs which makes explicit the sources of one’s knowledge and belief. The next three papers push the interplay between SL and DEL further, this time by showing that information dynamics, especially in a social situations, provides a natural foundation for substructural consequence relations, and which, on the other hand, supplies concrete tools to handle the nonstandard proof-theoretic behaviour of DEL. This idea goes back at least to [7, chap. 7], and has been picked up more recently, c.f. [8], and Aucher’s work on so-called DEL-sequent [1]. Roy and Hjortland’s contribution extend this work to the dynamic of soft information proposed by Baltag and smets [2]. Aucher himself contributes the next two papers, where he turns to substructural logics more generally and shows deep connections with models of information update changes. His first paper shows that a natural generalization of a classical substructural framework allows a direct construction of the Routhley–Meyer ternary relation using information updates. The second paper applies this insight to the special case of DEL. Taken together, Aucher’s papers not only provide a concrete, informational foundation for sub-structural connectives, but also answer a long-standing open question regarding the possibility of providing a well-behaved proof theory for DEL. The proof-theoretic investigation of DEL in a sub-structural framework is pursued further by the three papers of Frittella et al., which close the issue. As in Aucher’s first paper, all three use the resources of Belnap’s display logic [3] in order to provide cut-free proof systems for DEL. The first of their papers starts with a generalization of Belnap’s ‘automatic’ cut-elimination theorem, arguably the most celebrated feature of display logic, and then applies it to extend and generalize earlier work by Greco et al. on the proof theory of DEL [4]. The second paper provides an alternative proof system