We give a sound and complete axiomatization of a probabilistic extension of intuitionistic logic. Reasoning with probability operators is also intuitionistic (in contradistinction to other works on this topic), i.e., measure functions used for modeling probability operators are partial functions. Finally, we present a decision procedure for our logic, which is a combination of linear programming and an intuitionistic tableaux method.

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image. (shrink)

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image. (shrink)

The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend |$\textbf {PTEL}$| to axiomatize the corresponding first-order logic.

We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form $$\langle H, \mu \rangle $$ that needs not be a probability space. More precisely, though H needs not be a Boolean algebra, the corresponding monotone function (we call it measure) $$\mu : H \longrightarrow [0,1]_{\mathbb {Q}}$$ satisfies the following condition: if $$\alpha $$, $$\beta $$, $$\alpha \wedge \beta $$, (...) $$\alpha \vee \beta \in H$$, then $$\mu (\alpha \vee \beta ) = \mu (\alpha ) + \mu (\beta ) - \mu (\alpha \wedge \beta )$$. Since the range of $$\mu $$ is the set $$[0,1]_{\mathbb {Q}}$$ of rational numbers from the real unit interval, our logic is not compact. In order to obtain a strong complete axiomatization, we introduce an infinitary inference rule with a countable set of premises. The main technical results are the proofs of strong completeness and decidability. (shrink)

In this paper we present two families of probability logics (denoted _QLP_ and \(QLP^{ORT}\) ) suitable for reasoning about quantum observations. Assume that \(\alpha \) means “O = a”. The notion of measuring of an observable _O_ can be expressed using formulas of the form \(\square \lozenge \alpha \) which intuitively means “if we measure _O_ we obtain \(\alpha \) ”. In that way, instead of non-distributive structures (i.e., non-distributive lattices), it is possible to relay on classical logic extended with (...) the corresponding modal laws for the modal logic \({\textbf{B}}\). We consider probability formulas of the form \(CS_{z_{1},\rho _{1}; \ldots ; z_{m},\rho _{m}} \square \lozenge \alpha \) related to an observable _O_ and a possible world (vector) _w_: if _a_ is an eigenvalue of _O_, \(w_{1}\),..., \(w_{m}\) form a base of a closed subspace of the considered Hilbert space which corresponds to eigenvalue _a_, and if _w_ is a linear combination of the basis vectors such that \(w=c_{1}\cdot w_{1}+ \cdots + c_{m}\cdot w_{m}\) for some \(c_{i}\in {\mathbb {C}}\), then \(\Vert c_{1}-z_{1}\Vert \le \rho _{1}\),..., \(\Vert c_{m}-z_{m}\Vert \le \rho _{m}\), and the probability of obtaining _a_ while measuring _O_ in the state _w_ is equal to \(\Sigma _{i=1}^{m}\Vert c_{i}\Vert ^{2}\). Formulas are interpreted in reflexive and symmetric Kripke models equipped with probability distributions over families of subsets of possible worlds that are orthocomplemented lattices, while for \(QLP^{ORT}\) also satisfy ortomodularity. We give infinitary axiomatizations, prove the corresponding soundness and strong completeness theorems, and also decidability for _QLP_-logics. (shrink)

In this paper we present two types of logics and \ ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance between the probabilities of (...) α and β is less than or equal to ρ”, respectively. Logics of the later type formalize processes of thinking where information are coded by p-adic numbers. We use the same operators as above, but in this formalism K r,ρ α means “the p-adic code of the information α belongs to the p-adic ball with the center r and the radius ρ”, while D ρ α,β means “the p-adic distance between codes of α and β are less than or equal to ρ”. The corresponding strongly complete axiom systems are presented and decidability of the satisfiability problem for each logic is proved. (shrink)

We study a propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| with both future and past temporal operators, with non-rigid set of agents and the operators for agents’ knowledge and for common knowledge and with probabilities defined on the sets of runs and on the sets of possible worlds. A semantics is given by a class |${\scriptsize{\rm Mod}}$| of Kripke-like models with possible worlds. We prove decidability of |$\textbf {PTEL}$| by showing that checking satisfiability of a formula in |${\scriptsize{\rm Mod}}$| is (...) equivalent to checking its satisfiability in a finite set of finitely representable structures. The same procedure can be applied to the class of all synchronous |${\scriptsize{\rm Mod}}$|-models. We give an upper complexity bound for the satisfiability problem for |${\scriptsize{\rm Mod}}$|⁠. (shrink)

This paper is interested in commodity fetishism as a signal of collapsing marital mandates in the genre of lad lit. Instead of focusing solely on its late twentieth-century moment of emergence as a response to chick lit, the paper proposes a longer historical view in order to understand the crisis of masculinity that lad lit lays bare in its protagonists’ inherently queer status as collectors. The analysis puts critical pressure on the collectible object by re-reading the “lad” through the literary (...) figure of the fop, who represents a recurring response to similar crises in gender from the seventeenth-century’s comedy of manners to the novels of Jane Austen. The fop’s overinvestment in style and consequent marginalization is considered in Nick Hornby’s novels High Fidelity and About a Boy, in which the protagonists’ obsessive collecting of objects can be understood as both a dominant feature of their masculinity and the roadblock to their participation in heteronormative rituals of romance. Instead of reading Hornby’s characters as straightforwardly queer, this paper focuses on the commodity as a signal of queerness, and in turn its central role in the creation of, and the challenge to, the lad’s masculinity. (shrink)

This short enquiry investigates the relationships between knowledge of English and attitude towards the English language as held by Japanese university students. The goal of this study was to gain a better understanding of how attitude affects the learning of English and whether gender or geographic location of a student ’s hometown plays a role. A random sample of 85 participants completed a 26 item questionnaire which measured background information, attitude to English and knowledge of English. The difference in English (...) knowledge over several prefectures was tested using ANOVA and the results indicated that there was no statistical difference observed. Difference in attitude to English between male and female students was tested using a t-test and no statistical difference was observed. Pearson Correlation was used to test for any relationship between knowledge and attitude to English, but again no statistical different relationship was found. In addition , Multiple Regression was used to determine if there was a linear relationship between knowledge of English, and the 3 variables attitude to English, gender and prefecture. Again there was no statistically significant linear relationship between these variable. (shrink)

This paper represents an attempt to better understand the educational expectations of Japanese university students. Eighty students were asked to indicate whether or not they felt there was some relationship between 24 English words. The results were then added and entered into a table where the number at each intersection of words represented the total number of students that felt there relationship between those two words. This table was then analyzed using Multidimensional Scaling to produce a two dimension plot representing (...) the relationship between these 24 words. Since the distance between the words the plot represents the level of similarity, a study of the result gives some insight into the educational expectations of these students. A description of the data collection and analysis, as well as, one possible interpretation of the results is included. (shrink)

This paper presents the results of an attempt to adapt the technology acceptance model to a questionnaire to indicate whether or not the Moodle content management system was accepted by 147 Japanese University English language students. The questionnaire consisted of 13 items based on the factors of usefulness and ease-of-use. A factor analysis was performed on the results to ensure the number of underlying factors explaining the data. The result indicated that 2 factors explained more than 94% of item variation. (...) In addition, a discussion of the individual participant answers demonstrated that more than 85% of participants of this study accepted the Moodle system as both useful and easy to use. (shrink)

A normalizable natural deduction formulation, with subformula property, of the implicative fragment of classical logic is presented. A traditional notion of normal deduction is adapted and the corresponding weak normalization theorem is proved. An embedding of the classical logic into the intuitionistic logic, restricted on propositional implicational language, is described as well. We believe that this multiple-conclusion approach places the classical logic in the same plane with the intuitionistic logic, from the proof-theoretical viewpoint.

Participation in deliberation in stable democracies produces effects which are beneficial for democracy, while the results of deliberative innovations in non-democracies are more ambiguous. This article contributes to the debate about the effects of participatory democratic innovations on attitudes, related to democratic commitments, political capacities and political participation, in the increasingly ubiquitous hybrid regimes. We present the evidence collected from the participants before and after deliberative mini publics (DMPs), held in Serbia in 2020. Serbia is an exemplary case of a (...) recent wave of autocratization, which had led to it becoming a hybrid regime, and it had no track record of deliberative innovations. When conducting the mini publics, we introduced an innovation in the standard design, by including active citizens - representatives of local initiatives or social movements particularly interested in the issue of DMPs. We could not find evidence that the democratic innovation affected attitudes of participants regarding democratic commitments, political capacities and political participation. However, we did find that participants of the DMPs became less satisfied with the functioning of the democracy on the local level. We argue that the anti-democratic wider context of hybrid regimes can produce adverse effects when introducing participatory democratic innovations, at least when it comes to this specific dimension of political participation. We conclude with the suggestions for further research, and a call for consideration of the wider political context when designing democratic interventions in hybrid regimes. (shrink)

Political discourse is primarily identified as political action, the discourse of deliberating which course of action to follow in accordance with specific political goals. A pragmatic analysis of various sub-genres of political discourse can identify the preference for particular speech acts. The first aim of this paper is to analyze commissive and expressive illocutionary acts in political speeches, as indicators of personal involvement of political speakers, notorious for vagueness and avoiding commitment. A corpus of Serbian, American and British political speeches (...) that address the issue of economic standard of living has been examined to identify commissive illocutionary acts as indicators of politicians’ explicit commitment to a chosen course of action, and expressive illocutionary acts as indicators of politicians’ explicit attitudes to their own or other politicians’ chosen practices. The analysis classifies subtypes of commissives and expressives in the corpus and identifies illocutionary force indicating devices that constitute them in English and in Serbian, after which the resulting classifications are compared and contrasted. The research results are aimed at explaining the hypothesis that a specific use/lack of commissives and expressives can be the politician’s strategy for adding credibility to their speeches, and in that way, swaying public opinion to serve the politician’s interest; conversely, establishing the relation between the use/lack of these illocutionary acts and the politician’s commitment to actions can be a method for exposing the politician’s lack of credibility and accountability. (shrink)

This paper presents a sequent calculus for the positive relevant logic with necessity and a proof that it admits the elimination of cut.

Let $\mathcal M=$ be a linearly ordered first-order structure and T its complete theory. We investigate conditions for T that could guarantee that $\mathcal M$ is not much more complex than some colored orders. Motivated by Rubin’s work [5], we label three conditions expressing properties of types of T and/or automorphisms of models of T. We prove several results which indicate the “geometric” simplicity of definable sets in models of theories satisfying these conditions. For example, we prove that the strongest (...) condition characterizes, up to definitional equivalence, theories of colored orders expanded by equivalence relations with convex classes. (shrink)

In Ilić and Boričić, the right-handed cut-free sequent calculus $GRW$ for the contraction-less relevant logic $RW$ is defined. In this paper, we show that the enlargement of the system $GRW$ with the structural rule of intensional contraction presents the sequent system for the principal relevant logic $R$ but the rule of cut cannot be eliminated in $GRW+$.

In 1965, Claude Chabrol created La Muette – a fifteen-minute homage to Paris’s sixteenth district. In this short movie, Chabrol uses silence to ask some fundamental questions about the nature of human coexistence: the movie is seen, or better heard, from the perspective of a boy who, ignored by his parents, does not manage to say a word throughout; provoked by this imposed restriction, the boy decides to become not only “mute” but also “deaf.” His decision, however, results in tragic (...) consequences. In La Muette, Chabrol reminds us that the question of coexistence already posed by Virgil in his Eclogues, and signified by sound that freely resounds, has never ceased to be asked. In this Collision, I use the term “post-pastoral” to connect Virgil and Chabrol, and to open a discussion on sonically signified freedom. (shrink)

A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.

In our paper [3], a sequent system for the contraction‐less positive relevant logic with co‐tenability,, is considered. Its sequent system with the rule of cut, which does not involve the truth constant t, is presented, and the proof that it admits the elimination of cut is given. However, in the proof of the cut‐elimination theorem some forms of proofs, which may cause difficulties for the cut‐elimination argument, are not considered. The purpose of this paper is to present them and to (...) re‐prove that admits the elimination of cut. (shrink)

We introduce a notion of simplicity for types in discretely ordered first order structures. We prove that all the structure on the locus of a simple type is induced exclusively by the ordering relation. As an application we determine all possible expansions of satisfying CB = 1.

Academic engagement describes students’ involvement in academic learning and achievement. This paper reports the psychometric properties of the University Student Engagement Inventory (USEI) with a sample of 3992 university students from nine different countries and regions from Europe, North and South America, Africa, and Asia. The USEI operationalizes a trifactorial conceptualization of academic engagement (behavioral, emotional and cognitive). Construct validity was assessed by means of confirmatory factor analysis and reliability was assessed using Cronbach’s alpha and McDonald’s omega coefficients. Weak measurement (...) invariance was observed for country/region, while strong measurement invariance was observed for gender and area of graduation. The USEI scores showed predictive validity for dropout intention, self-rated academic performance, and course approval rate while divergent validity with student burnout scores was also evident. Overall, the results indicate that the USEI can produce reliable and valid data on academic engagement of university students across the world. (shrink)