Goal of research
The project aims to develop a conceptually unified models of the rational agency which would allow to formally explicate contemporary and classical approaches to the problems of metaphysics, epistemology, logic, and linguistic pragmatics.
The traditional logical, philosophical, and linguistic approaches were enriched with the methodological tools of (1) dynamic epistemic logic; (2) game theory; (3) semantics of possible worlds; (4) constructive theory of types; (5) formal phenomenology; (6) univalent foundations of mathematics, (7) speech act theory and post-Gricean pragmatics, (8) corpus methods; (9) experimental psycholinguistic methods (stimulus pictures, fillers, statistical processing of results using the Kruskal–Wallis one-way analysis of variance and Wilcoxon signed-rank test).
Empirical base of research
The results of linguistic experiments with native speakers of Russian language.
Results of research:
A new approach to the understanding of the notion of joint attention based on the cognitive notions of common knowledge and common awareness has been proposed. It has been argued that an alternative approach based on the notion of a fundamentally primitive phenomenon of sensory experience is not sufficient for an analysis of joint attention. The advantage of the proposed approach is that it allows one to combine the perceptual conditions for the functioning of joint attention with doxatic conditions.
The completeness and decidability of the extensions of canonical logics with the modality of the (reflexive) transitive closure have been proved. It has been shown that the logic of an infinitary operator of almost necessity is not closed under the substitution rule, and thus does not belong to normal modal logic. It is proved that in the lattice of logics of an infinitary operator of almost necessity there is one maximal logic. The research of relational, topological, and mixed topo-relational semantics for a bimodal language has been conducted. A finite axiomatization of the modal logic S4DT0 has been constructed. The completeness of this logic with respect to the class of all topological spaces TO and its decidability have been proved.
A universal method for transforming a winning strategy in a semantic game into a winning strategy in a provability game has been developed. Four formal systems have been constructed: two for a public announcement in intuitionistic logic and two for a public announcement in intuitionistic epistemic logic (IEL). For each system, the Hilbert-type axiomatics and Kripke semantics are proposed. The correctness and completeness of these systems have been proved. A solution to the paradox of becoming in the framework of a substructural logic without the rule of contraction has been proposed.
A logical model for epistemic agents with budgetary constraints that describes the dynamics of resource-dependent knowledge in multi-agent systems has been constructed. The solution to the lottery paradox based on this model has been proposed. It has been shown that the lottery paradox involves resource-dependent knowledge, and the structure of this knowledge can be explicated through a dynamic model of quantification based on the resource-dependent statements. It has been proved that finding the least manipulated rule of voting is not a universal problem: each rule can show the lowest value of the manipulability index depending on the combination of the input parameters. A new model and method of estimation of argument propagation that helps to analyze the influence of employees’ social interactions on different kinds of business processes have been constructed. Parameters of Erdos-Renie model, Watts-Strogatz model, Barabasi-Albert model for the real datasets have been found. The bifurcation-like and chaotic-like types of the distributions of the arguments between the employees have been shown. Two main scenarios of the distribution of the arguments have been defined: the infimum of the number of employees who accepted the argument and the supremum of the number of employees who accepted the argument.
Differences and essential characteristics of expressively equivalent logical notations have been demonstrated. It has been shown that the essential differences between expressively equivalent logical notations imply the possibility of "multiple readings" of formulas that depend on a variety of characteristics of a particular notational system: its vocabulary, linearity or non-linearity, and tabularity or non-tabularity. The principles of demarcation between formal and material consequence in the history of logic are systematized. The differences between Tarski’s classical dichotomy of formal and material consequence, on the one hand, and the contemporary model-theoretical approaches to consequence, the dichotomies of consequentia formalis and consequentia materialis in John Buridan’s logic, formal and material grounding in Bernard Bolzano’s theory of science, material and logical leading principles of reasoning in Charles S. Peirce’s classification of arguments, on the other, have been shown. It has been proved that the shift of attention from truth conditions towards the relation of grounding might offer important insights into the dynamic taxonomies of consequences and other logical relations.
A constructive approach to the logical reconstruction of scientific theories based on the idea of methods as the fundamental elements of scientific theories has been developed. This approach provides a rigorous formal way to conceptualize the idea of the inevitable load of theoretical assumptions in scientific experiments and observations, as well as to analyze the formal structure of the relevant concepts. The conceptual dependence of formal mathematical proofs on informal elements of mathematical practice is demonstrated on the example of the mutilated chessboard problem.
The presuppositions and tendencies that defined the emergence of logical pluralism in Lvov-Warsaw school have been revealed. It has been shown that the logical pluralism emerged from the orientation to logic and logical methods when solving the complex philosophical issues, the paraphrasing method and awareness by school representatives of an impossibility of overcoming paralogisms of classical philosophical theories in the framework of classical logic. The conceptual background of the methodology of conceptual engineering has been defined. Various kinds of motivation to pursue this strand of philosophical methodology have been described. It has been demonstrated that the methods of conceptual engineering are equally compatible with both revisionary and non-revisionary types of contemporary metaphilosophical approaches to philosophical methodology. The limitations of the radical post-Fregean anti-psychologistic approaches to the normativity of logic have been shown. In the context of the social studies of the neuro-diversity movement, it has been proved that the norm of reasoning in logic has a relational nature that significantly depends on the cultural practices involved in teaching this norm.
A two-stage approach to the explication of the formal semantic operator of widening is proposed. At the first stage, multiple interpretations are generated using the widening operator. At the second stage, single interpretations are obtained using the formal semantic operator of exhaustification. In the context of the problem of an over-specification of a number in the production of a reference, it has been shown that color is generally a more salient attribute than size, shape, pattern, and other attributes. At the same time, it has been experimentally demonstrated that the small size is an even more salient attribute than color. The fruitfulness of the convergence of topological and mereological approaches to the logical representation of auditory perception has been demonstrated.
The project has resulted in 12 articles that have been published in a peer-reviewed journal, indexed in the Web of Science and/or Scopus databases (3 articles in Q1-Q2 WoS, 5 articles in Q3-Q4 WoS, 3 articles in Q1 Scopus, 1 article in Q2 Scopus). The results of the project were presented at the Third international HSE Semantics & Pragmatics Workshop and at the international conference “Formal Philosophy”. Members of the project participated in the project as well as philosophers, mathematicians, linguists from Russia, Belarus, France, Great Britain, the Netherlands, Germany, Israel, Poland, Spain, Italy, Israel, the USA, and Japan. Three seminars were working as a part of the project: the theoretical seminar “Formal Philosophy” (5 meetings), the research seminar “From the Logical Point of View” (20 meetings), the educational seminar “Logical Semantics” (10 meetings). The results of the project were also approbated in 12 reports of its participants at conferences and theoretical seminars at universities and research centers across the world.
Level of implementation, recommendations on implementation or outcomes of the implementation of the results
The results of the research have been used in the teaching courses on logic, philosophy of language, history of philosophy, theory of language, cross-cultural pragmatics, contemporary Russian language, and the elective course “Formal and experimental pragmatics”. The results have also been employed to develop the research seminar “Logic and analytic philosophy” for the educational program “Philosophy” at the Faculty of Humanities, HSE. The topics of the research have been reflected in a large number of student’s course papers, undergraduate and graduate theses at the HSE Faculty of Humanities.