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Proponents of model-theoretic logical inferentialism defend the view that the meaning of logical vocabulary, such as the truth functions associated with conjunction or negation, is determined by their inferential use. This position provides a naturalist and empiricist account of the meaning of logical vocabulary, since inferences consist of concrete speech acts that can be observed, such as assertions and denials. As a consequence, model-theoretic inferentialism gives an account of a problem widely discussed in philosophy of language as well as cognitive science for the meaning of logical vocabulary, that is, it provides an account of meaning based on the use of language. In this dissertation, we provide a model-theoretic logical inferentialist account to three-valued Strong Kleene Logics. In particular, we will show various solutions to the categoricity problem regarding these logics in order to show that we can determine the intended models of these logics from their inferences, we will give a model-theoretic logical inferentialist account to Quine [94]'s challenge ``Do proponents of different logics talk past each other, i.e., does the meaning of logical operators change when logics change?", and last we will give an account of Prior [93]'s challenge of tonk to inferentialism.In Chapter 1, we introduce model-thereotic logical inferentialism, and we introduce the technical machinery to determine the inferential semantics from a logic. In Chapter 2, we show how we can determine the intended semantics of Classical Logic and a class of Strong Kleene logics. In other words, we provide a number of well-motivated solutions to the categoricity problem, also known as Carnap's problem, regarding these logics. In Chapter 3, we provide a model-theoretic logical inferentialist account Quine [94]'s question: Do proponents of different logics talk past each other, i.e., does the meaning of logical operators change when logics change? We argue that model-theoretic inferentialists can provide an alternative account to this problem in comparison to the traditional model-theoretic or proof-theoretic accounts, since model-theoretic inferentialists use the inferential semantics of a logic. Chapter 4, we discuss the problem of tonk from a model-theoretic logical inferentialist point of view. We first introduce different tonk-like logical operators in our metainferential system, and define notions of metainferential existence and metainferential uniqueness. Then, we argue that the solution discussed by Fjellstad [39] is favored by model-theoretic logical inferentialist, given that the non-determinate interpretation of tonk discussed in Teijeiro [126] does not yield a completeness result when tonk-like connectives are introduced to our metainferential systems. Then, we argue that the substructural solution to tonk cannot be generalized to all logical operators.

Building on early work by Girard (1987) and using closely related techniques from the proof theory of many-valued logics, we propose a sequent calculus capturing a hierarchy of notions of satisfaction based on the Strong Kleene matrices introduced by Barrio et al. (Journal of Philosophical Logic 49:93–120, 2020) and others. The calculus allows one to establish and generalize in a very natural manner several recent results, such as the coincidence of some of these notions with their classical counterparts, and the possibility of expressing some notions of satisfaction for higher-level inferences using notions of satisfaction for inferences of lower level. We also show that at each level all notions of satisfaction considered are pairwise distinct and we address some remarks on the possible significance of this (huge) number of notions of consequence.

In this paper we discuss sequent calculi for the propositional fragment of the logic of HYPE. The logic of HYPE was recently suggested by Leitgeb (Journal of Philosophical Logic 48:305–405, 2019) as a logic for hyperintensional contexts. On the one hand we introduce a simple $$\mathbf{G1}$$ G 1 -system employing rules of contraposition. On the other hand we present a $$\mathbf{G3}$$ G 3 -system with an admissible rule of contraposition. Both systems are equivalent as well as sound and complete proof-system of HYPE. In order to provide a cut-elimination procedure, we expand the calculus by connections as introduced in Kashima and Shimura (Mathematical Logic Quarterly 40:153–172, 1994).

In The Form of Truth: Hegel’s Philosophical Logic, Elena Ficara offers a reappraisal of G.W.F. Hegel’s logic within the history of logic and in relation to the logics of today. She brings together ...

In order to reply to the contemporary skeptic’s argument for the conclusion that we don’t have any empirical knowledge about the external world, several authors have proposed different fallibilist theories of knowledge that reject the epistemic closure principle. Holliday (Journal of Philosophical Logic, 44(1), 1–62 2015a), however, shows that almost all of them suffer from either the problem of containment or the problem of vacuous knowledge or both. Furthermore, Holliday (2015b) suggests that the fallibilist should allow a proposition to have multiple sets of relevant alternatives, each of which is sufficient while none is necessary, if all its members are eliminated, for knowing that proposition. Not completely satisfied with Holliday’s multi-path reply to the skeptic, the author suggests a new single-path relevant-possibility theory of knowledge and argues that it can avoid both the problem of containment and the problem of vacuous knowledge of a certain sort while rejecting skepticism about the external world.

Barrio et al. (Journal of Philosophical Logic, 49(1), 93–120, 2020) and Pailos (Review of Symbolic Logic, 2020(2), 249–268, 2020) develop an approach to define various metainferential hierarchies on strong Kleene models by transferring the idea of distinct standards for premises and conclusions from inferences to metainferences. In particular, they focus on a hierarchy named the $\mathbb {S}\mathbb {T}$ S T -hierarchy where the inferential logic at the bottom of the hierarchy is the non-transitive logic ST but where each subsequent metainferential logic ‘says’ about the former logic that it is transitive. While Barrio et al. (2020) suggests that this hierarchy is such that each subsequent level ‘in some intuitive sense, more classical than’ the previous level, Pailos (2020) proposes an extension of the hierarchy through which a ‘fully classical’ metainferential logic can be defined. Both Barrio et al. (2020) and Pailos (2020) explore the hierarchy in terms of semantic definitions and every proof proceeds by a rather cumbersome reasoning about those semantic definitions. The aim of this paper is to present and illustrate the virtues of a proof-theoretic tool for reasoning about the $\mathbb {S}\mathbb {T}$ S T -hierarchy and the other metainferential hierarchies definable on strong Kleene models. Using the tool, this paper argues that each level in the $\mathbb {S}\mathbb {T}$ S T -hierarchy is non-classical to an equal extent and that the ‘fully classical’ metainferential logic is actually just the original non-transitive logic ST ‘in disguise’. The paper concludes with some remarks about how the various results about the $\mathbb {S}\mathbb {T}$ S T -hierarchy could be seen as a guide to help us imagine what a non-transitive metalogic for ST would tell us about ST. In particular, it teaches us that ST is from the perspective of ST as metatheory not only non-transitive but also transitive.