We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.

We introduce a multimodal logic for order of magnitude reasoning which considers a new logic-based alternative to the notion of closeness, we provide an axiom system and prove its soundness and completeness.

We present a formalization of some ideas from Chomsky [9] in the framework of multimodal type logical grammar.

Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the (...) combination of implicit definability and reducibility. The three notions of definability are characterized semantically using (modal) algebras. The use of algebras, rather than frames, is shown to be necessary for these characterizations. (shrink)

Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the (...) combination of implicit definability and reducibility. The three notions of definability are characterized semantically using algebras. The use of algebras, rather than frames, is shown to be necessary for these characterizations. (shrink)

ABSTRACT Two objects o1, o2 of an information system are said to be complementary with respect to attribute a if α(o1) = -α(o2), where α(o) is the set of values of attribute a assigned to o. They are said to be complementary with respect to a set of attributes A if they are complementary with respect to each attribute α ε A. A multi-modal logical language for reasoning about complementarity relations is presented, with modalities [A] and ?A? parameterised by subsets (...) of a given set ATTR of attributes. Two complete deduction system for the language are presented: a Rasiowa-Sikorski style system using signed formulae, and an equivalent sequent calculus system in Gentzen style complete for theories. (shrink)

This is a preface for the Special Issue on Multimodal Logics published in Logica Universalis, March 2013, Volume 7, Issue 1, pp 1-5.

We present a relational proof system in the style of dual tableaux for the relational logic associated with a multimodal propositional logic for order of magnitude qualitative reasoning with a bidirectional relation of negligibility. We study soundness and completeness of the proof system and we show how it can be used for verification of validity of formulas of the logic.

We present a proof system for a multimode and multimodal logic, which is based on our previous work on modal Martin-Löf type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e., a small 2-category. The logic is extended to a lambda calculus, establishing a Curry–Howard correspondence.

We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various non-classical logics. We report some experiments using the higher-order automated theorem prover LEO-II.

XML documents and, more generally, semistructured data, can be seen as labelled graphs. In this paper we set a correspondence between such graphs and the models of a language of hybrid multimodal logic. This allows us to characterize a schema for semistructured data as a formula of hybrid multimodal logic, and instances of the schema as models of this formula. We also investigate how to express in such a logic integrity constraints on semistructured data, in (...) particular some classes of constraints widely considered in the literature. The contribution of this work is twofold: 1) We generalize the notion of schema, by proposing a definition of schema were references are “well typed”. 2) We formalize semistructured data, schema for semistructured data and integrity constraints in a unique framework, namely hybrid multimodal logic. (shrink)

Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic above is -persistent and universal, the infinitary and predicate extension of with BF and BF is Kripke complete, where BF and BF denote the formulas pi pi and x x, respectively. The results include the completeness of extensions of standard modal logics such as , and its extensions by the schemata T, B, 4, 5, D, and their combinations. The (...) proof is obtained by extending the correspondence between the representation of modal algebras and the completeness of propositional modal logic to infinite. (shrink)

In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives /, *, \, together with a package of structural postulates characterizing the resource management properties of the * connective. Different choices for Associativity and Commutativity yield the familiar logics NL, L, NLP, LP. Semantically, a simple Lambek system is a unimodal logic: the connectives get (...) a Kripke style interpretation in terms of a single ternary accessibility relation modeling the notion of linguistic composition for each individual system.The simple systems each have their virtues in linguistic analysis. But none of them in isolation provides a basis for a full theory of grammar. In the second part of the paper, we consider two types of mixed Lambek systems.The first type is obtained by combining a number of unimodal systems into one multimodal logic. The combined multimodal logic is set up in such a way that the individual resource management properties of the constituting logics are preserved. But the inferential capacity of the mixed logic is greater than the sum of its component parts through the addition of interaction postulates, together with the corresponding interpretive constraints on frames, regulating the communication between the component logics.The second type of mixed system is obtained by generalizing the residuation scheme for binary connectives to families of n-ary connectives, and by putting together families, of different arities in one logic. We focus on residuation for unary connectives, hence on mixed frames, as these already represent the complexities in full. We prove a number of elementary logical results for unary families of residuated connectives and their combination with binary families. The existing proposals for unary ‘structural modalities’ are situated within this general framework, and a number of new linguistic applications is given. (shrink)

This paper shows that some classes of multimodal paraconsistent logics endowed with weak forms of negation are incompletable with respect to Kripke semantics. The reach of such incompleteness is discussed, and we argue that this shortcoming, more than just a logical predicament, may be relevant for attempts to characterize quantum logics and to handle quantum information and quantum computation.

Name der Zeitschrift: Semiotica Jahrgang: 2018 Heft: 220 Seiten: 95-121.

The problem of completeness for predicate modal logics is still under investigation, although some results have been obtained in the last few years . As far as we know, the case of multimodal logics has not been addressed at all. In this paper, we study the combination of modal logics in terms of combining their semantics. We demonstrate by a simple example that in this sense predicate modal logics are not so easily manipulated as propositional ones: mixing two Kripke-complete (...) predicate modal logics results in a Kripke-incomplete system. (shrink)

The analysis of multimodal argumentation in advertising is a crucial and problematic area of research. While its importance is growing in a time characterized by images and pictorial messages, the methods used for interpreting and reconstructing the structure of arguments expressed through verbal and visual means capture only isolated dimensions of this complex phenomenon. This paper intends to propose and illustrate a methodology for the reconstruction and analysis of “double-mode” arguments in advertisements, combining the instruments developed in social semiotics, (...) pragmatics, and argumentation theory. An advertisement is processed through a five-step path. The analysis of its context, text genre, and images leads to a first representation of the messages that it encodes both pictorially and verbally (step 1). These first semantic representations are further enriched by including their polyphonic articulations and presuppositions (step 2), their explicatures (step 3), and their dialogical functions and illocutionary forces (step 4). These pragmatic steps retrieve the commitment structure of the ad, which allows a further argument analysis conducted through argumentation schemes (step 5). (shrink)

In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives /,,\, together with a package of structural postulates characterizing the resource management properties of the connective.Different choices for Associativity and Commutativity yield the familiar logics NL, L, NLP, LP. Semantically, a simple Lambek system is a unimodal logic: the connectives get a Kripke style interpretation (...) in terms of a single ternary accessibility relation modeling the notion of linguistic composition for each individual system.The simple systems earch have their virtues in linguistic analysis. But none of them in isolation provides a basis for a full theory of grammar. In the second part of the paper, we consider two types of mixed Lambek systems. (shrink)

Digitization of every daily procedure requires trustworthy verification schemes. People tend to overlook the security of the passwords they use, i.e. they use the same password on different occasions, they neglect to change them periodically or they often forget them. This raises a major security issue, especially for elderly people who are not familiar with modern technology and its risks and challenges. To overcome these drawbacks, biometric factors were utilized, and nowadays, they have been widely adopted due to their convenience (...) of use and ease of hardware installation. Many biometric-based authentication schemes were proposed, but despite the advantages that they offer, recent research has shown that biometrics by itself cannot be considered as an inviolable technique. Recently, we have proposed StegoPass, a novel method that obtains the 68 facial points of a user and utilizes them as a stego message to an image. This produced stego image was the password. Although the experiments conducted showed maximum security, it would be challenging to enhance the robustness of the proposed model for even more attacks. This paper examines the utilization of multimodal biometrics as the secret message embedded in the image. More specifically, besides the extraction of the facial points, we extract the unique minutiae moments and combine them in a feature vector. This feature vector is then embedded in the image. Two different datasets were used, and the security of the method was tested against state-of-the-art deep learning models, i.e. generative adversarial networks, to test whether the image could be digitally synthesized and fool the proposed verification scheme. The results proved that the new enhanced version of StegoPass offers an extremely secure method as its predecessor. (shrink)

Our brains make up a series of signs and are engaged in making or manifesting or reacting to a series of signs: through this semiotic activity they are at the same time engaged in “being minds” and so in thinking intelligently. An important effect of this semiotic activity of brains is a continuous process of “externalization of the mind” that exhibits a new cognitive perspective on the mechanisms underling the semiotic emergence of abductive processes of meaning formation. To illustrate this (...) process I will take advantage of the analysis of some aspects of the cognitive interplay between internal and external representations. I consider this interplay critical in analyzing the relation between meaningful semiotic internal resources and devices and their dynamical interactions with the externalized semiotic materiality suitably stocked in the environment. Hence, minds are material, “extended” and artificial in themselves. A considerable part of human abductive thinking is occurring through an activity consisting in a kind of reification in the external environment and a subsequent re-projection and reinterpretation through new configurations of neural networks and chemical processes. I also illustrate how this activity takes advantage of hybrid representations and how it can nicely account for various processes of creative and selective abduction, bringing up the question of how multimodal aspects involving a full range of sensory modalities are important in hypothetical reasoning. (shrink)

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? (...) no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator. (shrink)

In this paper, we introduce a general technology, calledtaming, for finding well-behaved versions of well-investigated logics. Further, we state completeness, decidability, definability and interpolation results for a multimodal logic, calledarrow logic, with additional operators such as thedifference operator, andgraded modalities. Finally, we give a completeness proof for a strong version of arrow logic.

The aim of the present paper is to contribute to a better understanding of the role of heraldry, in particular of para-heraldic devices known as “badges”, in 15th-century England. The case chosen for examination is that of the white rose, one of the major badges of Edward IV. The data consists of four contemporary texts in which Edward is referred to as the “rose”, analysed against the background of the use of the white rose of York as a heraldic device. (...) This includes surviving artefacts ranging from effigies to stained glass to seals and manuscript illuminations, as well as contemporary descriptions and depictions of those artefacts. Using the methodological apparatus of cognitive linguistics, specifically the multimodal metaphor and metonymy analysis, the author examines the interplay between language and heraldry. The results show that while the primary function of the white rose and of other badges employed by Edward IV was to emphasize his heritage and thus invite a metonymic reading, the badge inspired other, metaphorical readings, which were employed rhetorically by his supporters. In this context, the concept of the badge may be reinterpreted as a metaphtonymy. The analysis supports the view of heraldry as an integral element of medieval society. From a semiotic perspective, heraldry should be seen as a dynamic system that could be exploited creatively to suit the needs of its users, which in turn corresponds to the dynamic theory of metaphor. (shrink)

A system is classified as multimodal if its language has more than one modal operator as primitive, and such operators are not interdefinable. We extend the anodic and cathodic modal systems, introduced in Bueno-Soler and Bueno-Soler , to a class of the so-called basilar multimodal systems generating, in this way, the classes of anodic and cathodic multimodal logics. The cathodic multimodal systems are defined as extensions of positive multimodal systems by adding degrees of negation plus (...) consistency operators. In this way, cathodic multimodal systems are logics of formal inconsistency [the paraconsistent LFIs, as treated in Carnielli et al. ] enriched with multimodal operators. We focus the attention on models for such classes of systems and discuss how modal possible-translation semantics, as well as possible-worlds , can be defined to interpret basilar cathodic multimodal systems. While anodic systems are modeled by Kripke models only, we introduce the modal possible-translation models for cathodic systems. Such models, given by combinations of three-valued modal logics, besides their own interest, explain the role of non-trivializing contradictions in multimodal environment. (shrink)

Qualitative Reasoning (QR) is an area of research within Artificial Intelligence that automates reasoning and problem solving about the physical world. QR research aims to deal with representation and reasoning about continuous aspects of entities without the kind of precise quantitative information needed by conventional numerical analysis techniques. Order-of-magnitude Reasoning (OMR) is an approach in QR concerned with the analysis of physical systems in terms of relative magnitudes. In this paper we consider the logic OMR_N for order-of-magnitude reasoning with (...) the bidirectional negligibility relation. It is a multi-modal logic given by a Hilbert-style axiomatization that reflects properties and interactions of two basic accessibility relations (strict linear order and bidirectional negligibility). Although the logic was studied in many papers, nothing was known about its decidability. In the paper we prove decidability of OMR N by showing that the logic has the strong finite model property. (shrink)

We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.

In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.

There are two known general results on the finite model property of commutators [L0,L1]. If L is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both L0 and L1 are determined by transitive frames and have frames of arbitrarily large depth, then [L0,L1] does not have the fmp. In this paper we show that (...) commutators with a “weakly connected” component often lack the fmp. Our results imply that the above positive result does not generalize to universally axiomatizable component logics, and even commutators without “transitive” components such as [K3,K] can lack the fmp. We also generalize the above negative result to cases where one of the component logics has frames of depth one only, such as [S4.3,S5] and the decidable product logic S4.3×S5. We also show cases when already half of commutativity is enough to force infinite frames. (shrink)

ABSTRACT The goal of this paper is to improve heuristics for hard news discourse by proposing a cognitive model of abstraction, regarding social media contexts. To this end, hard news is discussed as a genre, structure and metalanguage, under the formal definition of a semiotic mode. Annotation is a successful technology to control the effects of genre operations, reveal relations, and to inquire about data and documents. It proceeds to characterize Twitter’s interface, in terms of formal and material regularities, employed (...) recursively. It further demonstrates the formalization of a semantics for hard news discourse in the so-called logical forms, which has been adapted from analytical tools developed by the Segmented Theory of Discourse Representation (SDRT) in order to examine coherence in different levels of detail. Finally, the implication of this approach as a discipline is discussed, regarding the production of transversal knowledge aiming at digital literacy, which urges in present times.1. (shrink)

This book shares the recent debates by systemic functional linguistics and other linguistic forums. Its principal focus is on how we use language to make meaning of the world, on how the systems and structures of the ideational function of language represent the realisation of our experiences of the world around us. The volume captures the endeavours of scholars working in different contexts, disciplines and languages around the world. Their contributions explore what underlies experiential and logical meaning-making through specific analyses (...) of recently-created, contextually diverse, single texts or collections of texts, from mono- to multimodal texts. The issues addressed are: layers of meaning through the transitivity system; agency and subjectivity; what kinds of participants and circumstances are associated with various processes and how these vary across languages; new ways of researching and capturing the interaction of the experiential function with the other functions of language - interpersonal, textual and logical - in communicative contexts; how multimodality and new ways of modelling experience semiotically influence the work of linguists, linguistic description and application. The book displays the dynamic dialogue on theoretical and applied interests of scholars interested in functional linguistics and working in a wide range of academic contexts. At post-graduate level advanced students will benefit from new perspectives, the innovative thinking and research accounts that make up the collection. The papers highlight the flexibility of systemic functional linguistic approach and exemplify how it can offer deeper and further insights into potential ways of exploring meaning-making by drawing on recent seminal developments in ideation. (shrink)

In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics (...) from these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators. (shrink)

In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics (...) from these classes have the finite model property with respect to the class of ♦-formulae, i.e. each ♦-formula has a ℒ-model iff it has a finite ℒ-model. Roughly speaking, a ♦-formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...) iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

We consider the problem of axiomatizing various natural "successor" logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the "standard" modal language (i.e. the language containing □ and ◊) is not finitely axiomatizable.

ABSTRACT In this paper we introduce and investigate various classes of multimodal logics based on frames with relative accessibility relations. We discuss their applicability to representation and analysis of incomplete information. We provide axiom systems for these logics and we prove their completeness.

I came to the topic of the title in connection with my logical investigations of the Is-Ought problem in multimodal logics . There are infinitely many mathematically possible modal logics. Are they all philosophically serious candidates? Which modal logic the “right” one — does such a question make sense? A similar question can be raised for the infinite variety of propositional logics weaker than classical logics. The Vienna Circle concept of logic was that logic holds merely (...) by form, independently from the facts of the world. Have we lost this concept completely? Is it a matter of arbitrary choice, of mere subjective-practical appropriateness, which logic one chooses? Is Quine right that there is no distinction between analytic and synthetic truth, even if we take “analytic truth” in the narrow sense of “logical truth”? These are the questions which have motivated this paper. (shrink)

A method is described for inducing a type-logical grammar from a sample of bare sentence trees which are annotated by lambda terms, called term-labelled trees . Any type logic from a permitted class of multimodal logics may be specified for use with the procedure, which induces the lexicon of the grammar including the grammatical categories. A first stage of semantic bootstrapping is performed, which induces a general form lexicon from the sample of term-labelled trees using Fulop’s (J Log (...) Lang Inf 14(1):49–86, 2005) procedure. Next we present a two-stage procedure for performing distributional learning by unifying the lexical types that are initially discovered. The first structural unification algorithm in essence unifies the initial family of sets of types so that the resulting grammar will generate all term-labelled trees that follow the usage patterns evident from the learning sample. Further altering the lexical categories to generate a recursively extended language can be accomplished by a second unification. The combined unification algorithm is shown to yield a new type-logical lexicon that extends the learning sample to a possibly infinite (and possibly context-sensitive) language in a principled fashion. Finally, the complete learning strategy is analyzed from the perspective of algorithmic learning theory; the range of the procedure is shown to be a class of term-labelled tree languages which is finitely learnable from good examples (Lange et al in Algorithmic learning theory, Vol 872 of lecture notes in artificial intelligence, Springer, Berlin, pp 423–437), and so is identifiable in the limit as a corollary. (shrink)

In this paper, we focus on a logical approach to the important notion of closeness, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals, which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We prove the decidability of the recently introduced multimodal logic for closeness and, then, we show (...) some capabilities of the logic with respect to expressivity in order to denote particular positions of the proximity intervals. (shrink)

We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of finite width, and a broader class of multimodal logics of ‘finite achronal width’ that are introduced here.

This article challenges the common view that improvements in critical thinking are best pursued by investigations in informal logic. From the perspective of research in psychology and neuroscience, hu-man inference is a process that is multimodal, parallel, and often emo-tional, which makes it unlike the linguistic, serial, and narrowly cog-nitive structure of arguments. At-tempts to improve inferential prac-tice need to consider psychological error tendencies, which are patterns of thinking that are natural for peo-ple but frequently lead to mistakes (...) in judgment. This article discusses two important but neglected error ten-dencies: motivated inference and fear-driven inference. (shrink)

Moore’s Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikka’s interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in a more (...) accurate way our logical intuitions about the notion of belief without sacrificing the possibility of providing an explanation for problematic cases such as Moore’s Paradox. (shrink)

Dynamic Topological Logic ( ) is a modal logic which combines spatial and temporal modalities for reasoning about dynamic topological systems , which are pairs consisting of a topological space X and a continuous function f : X → X . The function f is seen as a change in one unit of time; within one can model the long-term behavior of such systems as f is iterated. One class of dynamic topological systems where the long-term behavior of (...) f is particularly interesting is that of minimal systems ; these are dynamic topological systems which admit no proper, closed, f -invariant subsystems. In such systems the orbit of every point is dense, which within translates into a non-trivial interaction between spatial and temporal modalities. This interaction, however, turns out to make the logic simpler, and while s in general tend to be undecidable, interpreted over minimal systems we obtain decidability, although not in primitive recursive time; this is the main result that we prove in this paper. We also show that interpreted over minimal systems is incomplete for interpretations on relational Kripke frames and hence does not have the finite model property; however it does have a finite non-deterministic quasimodel property. Finally, we give a set of formulas of which characterizes the class of minimal systems within the class of dynamic topological systems, although we do not offer a full axiomatization for the logic. (shrink)

Let us consider multimodal logics and. We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and, we construct a connected frame which characterises the fusion. The frame thus obtained has some useful properties. Among others, is countable if both and are (...) countable, and there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point. We also describe a similar construction where we assume the existence of two classes consisting of rooted frames only. Using those classes and frames with so-called -roots, we construct a rooted frame adequate for the fusion of modal logics characterised by the classes under consideration. Both constructions can be used interchangeably. The selection of the construction depends on... (shrink)

This book focuses on dialog from a varied combination of fields: Linguistics, Philosophy of Language and Computation. It builds on the hypothesis that meaning in human communication arises at the discourse level rather than at the word level. The book offers a complex analytical framework and integration of the central areas of research around human communication. The content revolves around meaning but it also gives evidence of the connection among different points of view. Besides discussing issues of general interest to (...) the field, the book triggers theoretical argumentation that is currently under scientific discussion. It examines such topics as immanent reasoning joined with Recanati's lekta and free enrichment, challenges of internet conversation, inner dialogs, cognition and language, and the relation between assertion and denial. It proposes a dialogical framework for intra-negotiation and gives a geolinguistic perspective on spoken discourse. Finally, it examines dialog and abduction and sheds light on a generation of dialog contexts by means of multimodal logic applied to speech acts. (shrink)

The present article is devoted to a logical treatment of some fundamental concepts involved in responsibility attribution. We specify a theoretical framework based on a language of temporal deontic logic with agent-relative operators for deliberate causal contribution. The framework is endowed with a procedure to solve normative conflicts which arise from the assessment of different normative sources. We provide a characterization result for a basic system within this framework and illustrate how the concepts formalized can be put at work (...) in the analysis of examples of legal reasoning. (shrink)

The paper contains an exposition of standard ND-formalizations for modal logics. For the sake of simplicity, it is limited to propositional monomodal logics because focus is on methods not on logics. Some of the discussed approaches, however, may be easily extended to first order modal logics of different sorts or to multimodal logics . Natural Deduction is understood in the strict sense, explained below; neither Gentzen Sequent Calculus, nor Tableau Systems belong to that group. Moreover, some ND-systems with generalized (...) apparatus, like [2] or [3] are also omitted in this survey. There are four basic approaches to modality via NDformalization, which are compared and evaluated with respect to their generality: modalization of assumptions, modalization of reiteration rule, modalization of rules, application of modal assumptions. We focus on practical matters, especially on the applicability of discussed approaches, the only exception is the discussion of independent rules for necessity and possibility in the last section. (shrink)

The simplest combination of unimodal logics \ into a bimodal logic is their fusion, \, axiomatized by the theorems of \. Shehtman introduced combinations that are not only bimodal, but two-dimensional: he defined 2-d Cartesian products of 1-d Kripke frames, using these Cartesian products to define the frame product \. Van Benthem, Bezhanishvili, ten Cate and Sarenac generalized Shehtman’s idea and introduced the topological product \, using Cartesian products of topological spaces rather than of Kripke frames. Frame products have (...) been extensively studied, but much less is known about topological products. The goal of the current paper is to give necessary and sufficient conditions for the topological product to match the frame product, for Kripke complete extensions of \. (shrink)

A lot of research has been done on the detection of mental workload using various bio-signals. Recently, deep learning has allowed for novel methods and results. A plethora of measurement modalities have proven to be valuable in this task, yet studies currently often only use a single modality to classify MWL. The goal of this research was to classify perceived mental workload using a deep neural network that flexibly makes use of multiple modalities, in order to allow for feature sharing (...) between modalities. To achieve this goal, an experiment was conducted in which MWL was simulated with the help of verbal logic puzzles. The puzzles came in five levels of difficulty and were presented in a random order. Participants had 1 h to solve as many puzzles as they could. Between puzzles, they gave a difficulty rating between 1 and 7, seven being the highest difficulty. Galvanic skin response, photoplethysmograms, functional near-infrared spectrograms and eye movements were collected simultaneously using LabStreamingLayer. Marker information from the puzzles was also streamed on LSL. We designed and evaluated a novel intermediate fusion multimodal DNN for the classification of PMWL using the aforementioned four modalities. Two main criteria that guided the design and implementation of our DNN are modularity and generalisability. We were able to classify PMWL within-level accurate on a seven-level workload scale using the aforementioned modalities. The model architecture allows for easy addition and removal of modalities without major structural implications because of the modular nature of the design. Furthermore, we showed that our neural network performed better when using multiple modalities, as opposed to a single modality. The dataset and code used in this paper are openly available. (shrink)