Utilitarian attitude and norm in the discourse of Russian nationalists (on the material of the social network “VKontakte”)

Expressions with the predicative “expediently” manifest as a regular means of realization of modality of necessity, which is diverse in the semantic characteristics. The article aims to determine the type of the meaning of necessity and the nature of potentiality contained in such expressions in the discourse of Russian nationalists in the social network “VKontakte”. The article employs the methods semantic and pragmatic analysis. The author describes the predicative “expediently” as a modal operator of necessity, and the structure of the situation of necessity reflected by the expressions in the specified pragmatic conditions. The author reveals the semantic characteristics of combination of the utilitarian and deontic modalities that recognize such forms as the norm. It is established that expressions with the predicative “expediently” in the discourse of Russian nationalists manifest as the target norms and norms of operational preference. Such examples, due to their semantic and pragmatic characteristics, are the traditional method for realization of the speech act of appeal. The obtained results can be used in linguistic expertise, as they represent the significant diagnostic attributes of speech act of appeal in the pragmatic conditions of sociopolitical discourse. The scientific novelty is consists in the fact that this article is first to characterize the expressions with the predicative “expediently” as the forms of realization of meaning of the norm, which are recognized as the speech act of appeal in the discourse of Russian nationalists.

Note on the Intuitionistic Logic of False Belief

In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\varphi$ is not satisfied in a given world, but we still believe in it (or we think that it should be accepted). Another interpretations are also possible: e.g. that we do not accept $\varphi$ but it is imposed on us by a kind of council or advisory board. From the mathematical point of view, the idea is expressed by an adequate form of modal operator $\mathsf{W}$ which is interpreted in relational frames with neighborhoods. We discuss monotonicity of forcing, soundness, completeness and several other issues. We present also some simple systems in which confirmation of previously accepted formula is modelled.

Efficient loop-check for multimodal KD45n logic

We introduce sequent calculus for multi-modal logic KD45n which uses efficient loop-check. Efficiency of the used loop-check is obtained by using marked modal operator squarei which is used as an alternative to sequent with histories ([2,3]).We use inference rules with or branches to make all rules invertible or semi-invertible. We showthe maximum height of the constructed derivation tree. Also polynomial space complexity is proved.

On Equivalence Relations Between Interpreted Languages, with an Application to Modal and First-Order Language

I examine notions of equivalence between logics (understood as languages interpreted model-theoretically) and develop two new ones that invoke not only the algebraic but also the string-theoretic structure of the underlying language. As an application, I show how to construe modal operator languages as what might be called typographical notational variants of bona fide first-order languages.

Mighty Knowledge

We often claim to know what might be—or probably is—the case. Modal knowledge along these lines creates a puzzle for information-sensitive semantics for epistemic modals. This paper develops a solution. We start with the idea that knowledge requires safe belief: a belief amounts to knowledge only if it could not easily have been held falsely. We then develop an interpretation of the modal operator in safety (could have) that allows it to non-trivially embed information-sensitive contents. The resulting theory avoids various paradoxes that arise from other accounts of modal knowledge. It also delivers plausible predictions about modal Gettier cases.

Quantified Temporal Alethic Boulesic Doxastic Logic

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of $$T \times W$$ T × W models, and the proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper.

Contrast, Verum Focus and Anaphora: The Case of et pourtant si/non in French

This study examines the anaphoric status of the sequence et pourtant si/non in French. This sequence displays some properties not only of TP-Ellipsis but also of propositional anaphora. Consequently, the antecedent of this sequence can be recovered by means of either type of anaphoric process. I argue that the salient and relevant antecedent is constrained by the presence of a modalized environment. I claim that the discursive marker pourtant is assimilated to a modal operator (Jayez 1988, Martin 1987) expressing discourse contrast between two propositions anchored in two possible worlds that are not contradictory. Polarity Particles (POLPARTS) involved in this sequence are analyzed as emphasizing the truth of a proposition. As such, they are conveying semantic contrast between two polarities, that of a salient and accessible discourse antecedent and that of the missing part after et pourtant si/non. This is how POLPARTS upgrade the Common Ground. I develop a focus-based account for Verum Focus, building on alternatives along the lines of Hardt & Romero (2004). I suggest that the scope of an epistemic operator (Romero & Han 2004) and the conditions of use are relevant in order to reconstruct the adequate antecedent, which is not possible in an analysis based solely on lexical insertion and upgrading the Question Under Discussion (qud) by conditions governing the felicitous use of et pourtant si/non.

Boolean negation and non-conservativity I: Relevant modal logics

Many relevant logics can be conservatively extended by Boolean negation. Mares showed, however, that E is a notable exception. Mares’ proof is by and large a rather involved model-theoretic one. This paper presents a much easier proof-theoretic proof which not only covers E but also generalizes so as to also cover relevant logics with a primitive modal operator added. It is shown that from even very weak relevant logics augmented by a weak K-ish modal operator, and up to the strong relevant logic R with a S5 modal operator, all fail to be conservatively extended by Boolean negation. The proof, therefore, also covers Meyer and Mares’ proof that NR—R with a primitive S4-modality added—also fails to be conservatively extended by Boolean negation.

Suppose and Tell

The book argues that our use of conditionals is governed by imperfectly reliable heuristics, in the psychological sense of fast and frugal (or quick and dirty) ways of assessing them. The primary heuristic is this: to assess ‘If A, C’, suppose A and on that basis assess C; whatever attitude you take to C conditionally on A (such as acceptance, rejection, or something in between) take unconditionally to ‘If A, C’. This heuristic yields both the equation of the probability of ‘If A, C’ with the conditional probability of C on A and standard natural deduction rules for the conditional. However, these results can be shown to make the heuristic implicitly inconsistent, and so less than fully reliable. There is also a secondary heuristic: pass conditionals freely from one context to another under normal conditions for acceptance of sentences on the basis of memory and testimony. The effect of the secondary heuristic is to undermine interpretations on which ‘if’ introduces a special kind of context-sensitivity. On the interpretation which makes best sense of the two heuristics, ‘if’ is simply the truth-functional conditional. Apparent counterexamples to truth-functionality are artefacts of reliance on the primary heuristic in cases where it is unreliable. The second half of the book concerns counterfactual conditionals, as expressed with ‘if’ and ‘would’. It argues that ‘would’ is an independently meaningful modal operator for contextually restricted necessity: the meaning of counterfactuals is simply that derived compositionally from the meanings of their constituents, including ‘if’ and ‘would’, making them contextually restricted strict conditionals.

Completeness by Modal Definitions. Application to the Epistemic Logic With Hypotheses

We investigate the variant of epistemic logic S5 for reasoning about knowledge under hypotheses. The logic is equipped with a modal operator of necessity that can be parameterized with a hypothesis representing background assumptions. The modal operator can be described as relative necessity and the resulting logic turns out to be a variant of Chellas’ Conditional Logic. We present an axiomatization of the logic and its extension with the common knowledge operator and distributed knowledge operator. We show that the logics are decidable, complete w.r.t. Kripke as well as topological structures. The topological completeness results are obtained by utilizing the Alexandroff connection between preorders and Alexandroff spaces.