In this paper we study logical bilateralism understood as a theory of two primitive derivability relations, namely provability and refutability, in a language devoid of a primitive strong negation and without a falsum constant, $\bot $, and a verum constant, $\top $. There is thus no negation that toggles between provability and refutability, and there are no primitive constants that are used to define an “implies falsity” negation and a “co-implies truth” co-negation. This reduction of expressive power notwithstanding, there remains some interaction between provability and refutability due to the presence of (i) a conditional and the refutability condition of conditionals and (ii) a co-implication and the provability condition of co-implications. Moreover, assuming a hyperconnexive understanding of refuting conditionals and a dual understanding of proving co-implications, neither non-trivial negation inconsistency nor hyperconnexivity is lost for unary negation connectives definable by means of certain surrogates of falsum and verum. Whilst a critical attitude towards $\bot $ and $\top $ can be justified by problematic aspects of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations for these constants, the aim to reduce the availability of a toggling negation and observations on undefinability may also give further reasons to abandon $\bot $ and $\top $.

This article provides an analysis of verum marking in the Tsimshianic language Gitksan. Original fieldwork data are provided to show that Gitksan verum is very similar in its distribution and discourse effects to English verum, but displays two interesting differences. First, Gitksan verum is not marked by focal stress, but by a dedicated particle (k'ap). Second, Gitksan verum does not require givenness of the core propositional material. I argue that when applied to a proposition p, k'ap is (a) disallowed discourse-initially or in answer to a wh-question; (b) felicitous when responding to a prior assertion or implication of ¬p; and (c) felicitous in other contexts only if there is prior controversy in the discourse about the truth of p. I show that the semantic contribution of the Gitksan verum particle can be captured by a discourse management analysis: verum(p) is licensed only when the speaker believes that some interlocutor is committed to ¬p.