The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.

The emphasis is on the research approach applied in the last monograph of Prof. Nikolay Milkov. It is about studying the early sources of analytical philosophy, and especially in German literature from the late nineteenth and early twentieth century, he dwells on the Bulgarian philosophers Dimitar Mihalchev and Tseko Torbov. Dimitar Mihalchev publishes in German a monograph “Philosophical Studies. A Contribution to the Critique of Modern Psychologism” (Leipzig, 1909), which J. Moore evaluated. Tseko Torbov is an assistant to (...) the neo-Kantian Leonard Nelson. Prof. Nikolay Milkov does not fail to mention these small presences of Bulgarian philosophers in the Western European intellectual panorama. (shrink)

The paper offers the foundations of the theory of information media. Information media are dynamical systems with additional macrostructure of information-carrying states and information-preserving transformations. The paper also defines the notion of information media network as a system of information media connected by information transformations. It is demonstrated that many standard examples of information-containing and processing systems are captured by the general notion of information medium. The paper uses the theory (and informal discussion) of information media to motivate a structural (...) approach to the information in media. The idea is that the notion of information transformation should be regarded as more primitive than the notion of informational state. Thus in information systems, especially in the context of information technology, information is secondary while information transformation is primary. (shrink)

This article provides an answer to the question: What is the function of cognition? By answering this question it becomes possible to investigate what are the simplest cognitive systems. It addresses the question by treating cognition as a solution to a design problem. It defines a nested sequence of design problems: (1) How can a system persist? (2) How can a system affect its environment to improve its persistence? (3) How can a system utilize better information from the environment to (...) select better actions? And, (4) How can a system reduce its inherent informational limitations to achieve more successful behavior? This provides a corresponding nested sequence of system classes: (1) autonomous systems, (2) (re)active autonomous systems, (3) informationally controlled autonomous systems (autonomous agents), and (4) cognitive systems. -/- This article provides the following characterization of cognition: The cognitive system is the set of mechanisms of an autonomous agent that (1) allow increase of the correlation and integration between the environment and the information system of the agent, so that (2) the agent can improve the selection of actions and thereby produce more successful behavior. -/- Finally, it shows that common cognitive capacities satisfy the characterization: learning, memory, representation, decision making, reasoning, attention, and communication. (shrink)

This paper addresses one of the fundamental problems of the philosophy of information: How does semantic information emerge within the underlying dynamics of the world?—the dynamical semantic information problem. It suggests that the canonical approach to semantic information that defines data before meaning and meaning before use is inadequate for pre-cognitive information media. Instead, we should follow a pragmatic approach to information where one defines the notion of information system as a special kind of purposeful system emerging within the underlying (...) dynamics of the world and define semantic information as the currency of the system. In this way, systems operating with semantic information can be viewed as patterns in the dynamics—semantic information is a dynamical system phenomenon of highly organized systems. In the simplest information systems, the syntax, semantics, and pragmatics of the information medium are co-defined. It proposes a new more general theory of information semantics that focuses on the interface role of the information states in the information system—the interface theory of meaning. Finally, with the new framework, it addresses the debate between weakly semantic and strongly semantic accounts of information, siding with the strongly semantic view because the pragmatic account developed here is a better generalization of it. (shrink)

Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.

Review on Vaclav Nemec, Marius Victorinus: The Consubstantiality of The Trinity OIKOYMENH, Prague, 2006.

We present a complete axiomatisation of the operator of projection onto state in the Duration Calculus relative to validity in DC without extending constructs. Projection onto state was introduced and studied extensively in our earlier works. We first establish the completeness of a system of axioms and proof rules for the operator relative to validity in the extension of DC by neighbourhood formulas, which express the neighbourhood values of boolean DC state expressions. By establishing a relatively complete axiomatisation for the (...) neighbourhood formulas in DC, we then achieve completeness of our system relative to basic DC. (shrink)

This article presents results from simulations studying the hypothesis that mechanisms for landmark-based navigation could have served as preadaptations for compositional language. It is argued that sharing directions would significantly have helped bridge the gap between general and language-specific cognitive faculties. A number of different levels of navigational and communicative abilities are considered, resulting in a range of possible evolutionary paths. The selective pressures for, resp. against, increased complexity in either faculty are then evaluated for a range of environments. The (...) study aims specifically to identify whether there is a viable evolutionary path leading to compositional language, and if so, under what circumstances. The results show that environmental conditions can render a step towards more complex communication either desirable or harmul, and suggest that very specific initial conditions and changes in the environment, resp. the ecological niche occupied, would have been needed to select for compositional language. Subject to these conditions, a (proto)language using order, but no hierarchical structure could evolve. This represents a middle ground, which brings closer hypotheses about syntax that have so far appeared difficult to reconcile. (shrink)

The review is for a new study by Prof. Veselin Petrov, which is dedicated to the application of A. Whitehead's philosophical ideas in education and learning. For the Anglo-American thinker, this is an area that is very important for the development of civilization and therefore devotes dozens of studies on this topic.

Name der Zeitschrift: Semiotica Jahrgang: 2015 Heft: 204 Seiten: 315-339.

A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.

In the article, I outline the main layers that are fundamental to the construction of Bulgarian political culture. At the beginning of the text, I clarify the concept of political culture. The examined layers are four: geographical, Balkan, Orthodox, and national. These layers, in particular, have a determining influence on the character of Bulgarian political culture in the modern history of Bulgaria.

In this paper we show how modal logic can be applied in the axiomatizations of some dynamic ontologies. As an example we consider the case of mereotopology, which is an extension of mereology with some relations of topological nature like contact relation. We show that in the modal extension of mereotopology we may define some new mereological and mereotopological relations with dynamic nature like stable part-of and stable contact. In some sense such “stable” relations can be considered as approximations of (...) the “essential relations” in the domain of mereotopology. (shrink)

We generalise an interval-related interpolation theorem about abstract-time Interval Temporal Logic, which was first obtained in [GUE 01]. The generalisation is based on the abstract-time variant of a projection operator in the Duration Calculus, which was introduced in [DAN 99] and later studied extensively in [GUE 02]. We propose a way to understand interpolation in the context of formal verification. We give an example showing that, unlike abstract-time ITL, DC does not have the Craig interpolation property in general, and establish (...) a special form of Craig interpolation for abstract-time DC. Explicit definability after Beth is known to be strongly related to Craig interpolation in general. We show a limitation of a different kind to the scope of Beth definability in ITL by a counterexample too. We call the generalisation of interval-related interpolation that we present projection-related interpolation. The DC-specific restrictions apply to it too. We show that both Craig and projection-related interpolation hold about the ⌈P⌉-subset of DC without such restrictions. Our proofs of these theorems for the ⌈P⌉-subset entail algorithms for the construction of the interpolants. (shrink)

Mereotopology is an extension of mereology with some relations of topological nature like contact. An algebraic counterpart of mereotopology is the notion of contact algebra which is a Boolean algebra whose elements are considered to denote spatial regions, extended with a binary relation of contact between regions. Although the language of contact algebra is quite expressive to define many useful mereological relations and mereotopological relations, there are, however, some interesting mereotopological relations which are not definable in it. Such are, for (...) instance, the relation of n-ary contact, internal connectedness and some others. To overcome this disadvantage, we introduce a generalisation of contact algebra, replacing the contact with a binary relation between finite sets of regions and a region, satisfying some formal properties of Tarski consequence relation. The obtained system is called sequent algebra, considered as an algebraic counterpart of a new mereotopology. We develop the topological representation theory for sequent algebras showing in this way certain correspondence between point-free and point-based models of space. As a by-product, we show how one logical relation in nature notion, Tarski consequence relation, may have also certain spatial meaning. (shrink)

We present a variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall. The cooperation modalities assume the use the distributed knowledge of coalitions and accordingly refer to perfect recall incomplete information strategies. We propose a model-checking algorithm for the logic. It is based on techniques for games with imperfect information and partially observable objectives, and involves deciding emptiness for automata on infinite trees. We also propose an axiomatic system and prove (...) its completeness for a rather expressive subset. As for the constructs left outside this completely axiomatised subset, we present axioms by which they can be defined in the subset on the class of models in which every state has finitely many successors and give a complete axiomatisation for a “flat” subset of the logic with these constructs included. (shrink)

Democratic governments might be required by law to disseminate information to the people. This is called governmental transparency. What is the burden of transparency? We propose a “pragmatic information theory of communication” that places information accessibility as a foundation of transparency. Using a game model—the Transparency Game—we show that the pragmatic theory is the only one that makes it difficult for governments to appear transparent while not actually being transparent. There are two important consequences of understanding transparency through the theory: (...) Accessible information must be actionable, and cognitive science plays a vital role in assessing the accessibility of information. These consequences can have implications for public policies that promote transparency. (shrink)

This paper is a continuation of [VAK 01]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to Roeper's notion of region-based topology [ROE 97]. The similarity between the local proximity spaces of Leader [LEA 67] and local connection algebras is emphasized. Machinery, analogous to that introduced by Efremovi?c [EFR 51],[EFR 52], Smirnov [SMI 52] and Leader [LEA 67] for proximity and local proximity spaces, is developed. (...) This permits us to give new proximity-type models of local connection algebras, to obtain a representation theorem for such algebras and to give a new shorter proof of the main theorem of Roeper's paper [ROE 97]. Finally, the notion of MVD-algebra is introduced. It is similar to Mormann's notion of enriched Boolean algebra [MOR 98], based on a single mereological relation of interior parthood. It is shown that MVD-algebras are equivalent to local connection algebras. This means that the connection relation and boundedness can be incorporated into one, mereological in nature relation. In this way a formalization of the Whiteheadian theory of space based on a single mereological relation is obtained. (shrink)

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...) are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in (...) this way a counterexample semantics of the logic in question and some of its natural extensions. Among the extensions which are near to the intuitionistic logic are the minimal logic with Nelson negation which is an extension of the Johansson's minimal logic with Nelson negation and its in a sense dual version — the co-minimal logic with Nelson negation. Among the extensions near to the classical logic are the well known 3-valued logic of Lukasiewicz, two 12-valued logics and one 48-valued logic. Standard questions for all these logics — decidability, Kripke-style semantics, complete axiomatizability, conservativeness are studied. At the end of the paper extensions based on a new connective of self-dual conjunction and an analog of the Lukasiewicz middle value ½ have also been considered. (shrink)

Gabbay's separation theorem about linear temporal logic with past has proved to be one of the most useful theoretical results in temporal logic. In this paper, we establish an analogous statement a...

This paper presents an w-completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (DQP), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.

This paper presents a new kind of interpolation theorems about Neighbourhood Logic and Interval Temporal Logic . Unlike Craig interpolation, which holds for these logics too, the new theorems treat the existence of interpolants which specify properties of selected intervals in the models of NL and ITL.

We use Concurrent Game Models (CGM) in which simple conditional promises are assigned the role of negotiation steps aiming to represent the formation of temporary coalitions and their agendas. By transforming these extended CGMs into equivalent CGMs with incomplete information, established methods for rational synthesis become enabled. The interpretation of promises is compatible with that of announcements as in dynamic epistemic logics. To accommodate requirements on plays that are written wrt the runs of the original model, we use temporal projection (...) that hides negotiation steps. (shrink)

One major fault line in foundational theories of cognition is between the so-called “representational” and “non-representational” theories. Is it possible to formulate an intermediate approach for a foundational theory of cognition by defining a conception of representation that may bridge the fault line? Such an account of representation, as well as an account of correspondence semantics, is offered here. The account extends previously developed agent-based pragmatic theories of semantic information, where meaning of an information state is defined by its interface (...) role, to a theory that accommodates a notion of representation and correspondence semantics. It is argued that the account can be used to develop an intermediate approach to cognition, by showing that the major sources of tension between “representational” and “non-representational” theories may be eased. (shrink)

In this paper, intuitionistic modal logics which do not admit the law of the excluded middle are studied. The main result is that there exista a continuum of such logics.

ABSTRACT The notion of n-dimensional arrow structure is introduced, which for n = 2 coincides with the notion of directed multi-graph. In part I of the paper several first-order and modal languages connected with arrow structures are studied and their expressive power is compared. Part II is devoted to the axiomatization of some arrow logics. At the end some further perspectives of ?arrow approach? are discussed.

The aim of this paper is to give new kinds of modal logics suitable for reasoning about regions in discrete spaces. We call them dynamic logics of the region-based theory of discrete spaces. These modal logics are linguistic restrictions of propositional dynamic logic with the global diamond E. Their formulas are equivalent to Boolean combinations of modal formulas like E(A ∧ ⟨α⟩ B) where A and B are Boolean terms and α is a relational term. Examining what we can say (...) about dynamic models when we use formulas to describe them, we successively address the axiomatization/completeness issue and the decidability/complexity issue of our dynamic logics of the region-based theory of discrete spaces. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called \emph{elementary}. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called \emph{canonical}. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (shrink)

Forensic evidence often involves an evaluation of whether two impressions were made by the same source, such as whether a fingerprint from a crime scene has detail in agreement with an impression taken from a suspect. Human experts currently outperform computer-based comparison systems, but the strength of the evidence exemplified by the observed detail in agreement must be evaluated against the possibility that some other individual may have created the crime scene impression. Therefore, the strongest evidence comes from features in (...) agreement that are also not shared with other impressions from other individuals. We characterize the nature of human expertise by applying two extant metrics to the images used in a fingerprint recognition task and use eye gaze data from experts to both tune and validate the models. The Attention via Information Maximization model quantifies the rarity of regions in the fingerprints to determine diagnosticity for purposes of excluding alternative sources. The CoVar model captures relationships between low-level features, mimicking properties of the early visual system. Both models produced classification and generalization performance in the 75%–80% range when classifying where experts tend to look. A validation study using regions identified by the AIM model as diagnostic demonstrates that human experts perform better when given regions of high diagnosticity. The computational nature of the metrics may help guard against wrongful convictions, as well as provide a quantitative measure of the strength of evidence in casework. (shrink)

This paper is devoted to the complete axiomatization of dynamic extensions of arrow logic based on a restriction of propositional dynamic logic with intersection. Our deductive systems contain an unorthodox inference rule: the inference rule of intersection. The proof of the completeness of our deductive systems uses the technique of the canonical model.

The development of the green policies of the European Union (EU) has established a framework in which national governments had to introduce environmental measures with serious social and economic consequences. The present article examines the relationship political initiative – environmental awareness – pro-environmental behavior through the prism of a specific case study related to the 2023 protests in Bulgaria against the closure of coal plants. The analysis of public attitudes and of media discourse reveals that the Bulgarian government avoided legitimizing (...) its decisions through ecological motivations. Low levels of trust in political institutions and the perceived lack of prestige of ecological issues are shifting research attention to the barriers to pro-environmental behavior in contemporary European societies. (shrink)

A new modal logic containing four dynamic modalities with the following informal reading is introduced: $${\square^\forall}$$ – always necessary , $${\square^\exists}$$ – sometimes necessary , and their duals – $${\diamondsuit^\forall}$$ – always possibly , and $${\diamondsuit^\exists}$$ – sometimes possibly . We present a complete axiomatization with respect to the intended formal semantics and prove decidability via fmp.

Rough polyadic modal logics, introduced in the paper, contain modal operators of many arguments with a relational semantics, based on the Pawlak's rough set theory. Rough set approach is developed as an alternative to the fuzzy set philosophy, and has many applications in different branches in Artificial Intelligence and theoretical computer science.

We propose a generalization of Sahlqvist formulas to polyadic modal languages by representing such languages in a combinatorial PDL style and thus, in particular, developing what we believe to be the right syntactic approach to Sahlqvist formulas at all. The class of polyadic Sahlqvist formulas PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

One of the important extensions of PDL is PDL with intersection of programs. We devote this paper to its complete axiomatization.