Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can force the existence of (...) infinite models and have undecidable satisfiability problems. (shrink)

Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the Sofia school , the method remains little known. In our view this has deprived temporal logic of a valuable tool.The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the first technical, the second conceptual. First, we show that hybridization gives rise to (...) well-behaved logics that exhibit an interesting synergy between modal and classical ideas. This synergy, obvious for hybrid languages with full first-order expressive strength, is demonstrated for a weaker local language capable of defining the Until operator; we provide a minimal axiomatization, and show that in a wide range of temporally interesting cases extended completeness results can be obtained automatically. Second, we argue that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed further. To illustrate this, we discuss the advantages and disadvantages of a simple hybrid language which can quantify over paths. (shrink)

The present-day languages and language situation of the Silk Road regions of Central Asia reflect the consequences of the former use of many different languages and the multilingual trading along these routes, as demonstrated by the existence today of a number of hybridized languages whose emergence may in part be attributable to the trading activities on the Silk Road. These languages have, until very recently, received little attention, if any, by linguistic scholars. It has been mainly (...) through the large Language Atlases project mentioned in note 1 below that interest has become focused on them. (shrink)

Like many sociocultural phenomena in Brazil, popular music, as everyone knows, is the result of a meeting of influences. It could almost be said that it is born a cross-breed, given the half-European, half-African origins of its best-known first genres, lundu, choro and maxixe. As a result of its history it comes under the sign of the Cannibalism, the metaphor invented by modernist writers in the 1920s to refer to the ‘ritual devouring’ by which Brazil assimilated foreign values and made (...) them its own.Caetano Veloso and Gilberto Gil readily used the concept of Cannibalism at the end of the 1960s, when they founded Tropicalismo, which claimed a mixture of genres, styles and arts as its basis, and married international pop music and Brazilian traditions, electric guitars and berimbau. Tropicalismo as such only lasted for a few months, but the ideas which it promoted profoundly marked contemporary Brazilian culture. Caetano Veloso returned to the history of this movement in Verdade Tropical, an autobiographical work in which he reveals his thoughts on a number of subjects close to his heart: music, the cinema, masters/teachers, friends, family, love, sexuality freedom, prison, exile, books, language, etc. For this author, composer, performer, actor, director, poet and prose writer, inveterate and voracious reader and incorrigible chatterbox, anything to do with human beings is fair game. For Caetano loves words, and loves to talk about words. As early as the acknowledgements page he praises Unamuno, the author, according to him, of comments which are “the most moving that a foreigner has ever written about the Portuguese language”. And in a chapter entitled ‘Língua’ he mentions not only the songs he has written in English and his interest in the Anglo-Saxon language, but also his attachment to Romance languages in general and Portuguese in particular. (shrink)

: In recent literature supporting a hybrid view between metaethical cognitivism and noncognitivist expressivism, much has been made of an analogy between moral terms and pejoratives. The analogy is based on the plausible idea that pejorative slurs are used to express both a descriptive belief and a negative attitude. The analogy looks promising insofar as it encourages the kinds of features we should want from a hybrid expressivist view for moral language. But the analogy between moral terms and (...) pejorative slurs is also problematic. In this paper, I argue for two main ways in which we should distinguish between two different types of pejorative terms: slurs, on the one hand, and what I call general pejorative terms, on the other. I examine the problems with the analogy between slurs and moral terms and conclude that general pejorative terms like ‘jerk’ are a better candidate on which to model the potential dual-use behavior of moral terms. So if hybrid theorists are looking for a dual-use model for moral language, they should be careful to base their analogies on general pejoratives, rather than slurs. (shrink)

In this essay, I propose a novel hybrid metanormative theory. According to this theory, speakers making normative claims express both cognitive and motivational attitudes in virtue of the constitutive norms of the particular speech acts they perform. This view has four principal virtues: it is consistent with traditional semantic theories, it supports a form of motivational judgment internalism that does justice to externalist intuitions, it illuminates the connection between normative language and normative thought, and it explains how speakers can (...) express different conative states when speaking in different normative domains. In the first section, I discuss the theories of Stephen Finlay and David Copp. I show that they each come very close to having it both ways but ultimately fail. Understanding the shortcomings of these views is instrumental to a clear presentation of my own Hybrid Speech Act theory in section two. In the final section, I demonstrate how my view achieves its four advantages. (shrink)

In this essay, I propose a novel hybrid metanormative theory. According to this theory, speakers making normative claims express both cognitive and motivational attitudes in virtue of the constitutive norms of the particular speech acts they perform. This view has four principal virtues: it is consistent with traditional semantic theories, it supports a form of motivational judgment internalism that does justice to externalist intuitions, it illuminates the connection between normative language and normative thought, and it explains how speakers can (...) express different conative states when speaking in different normative domains. In the first section, I discuss the theories of Stephen Finlay and David Copp. I show that they each come very close to having it both ways but ultimately fail. Understanding the shortcomings of these views is instrumental to a clear presentation of my own Hybrid Speech Act theory in section two. In the final section, I demonstrate how my view achieves its four advantages. (shrink)

User intent classification is a vital component of a question-answering system or a task-based dialogue system. In order to understand the goals of users’ questions or discourses, the system categorizes user text into a set of pre-defined user intent categories. User questions or discourses are usually short in length and lack sufficient context; thus, it is difficult to extract deep semantic information from these types of text and the accuracy of user intent classification may be affected. To better identify user (...) intents, this paper proposes a BERT-Cap hybrid neural network model with focal loss for user intent classification to capture user intents in dialogue. The model uses multiple transformer encoder blocks to encode user utterances and initializes encoder parameters with a pre-trained BERT. Then, it extracts essential features using a capsule network with dynamic routing after utterances encoding. Experiment results on four publicly available datasets show that our model BERT-Cap achieves a F1 score of 0.967 and an accuracy of 0.967, outperforming a number of baseline methods, indicating its effectiveness in user intent classification. (shrink)

Moral language displays a characteristic duality. On the one hand, moral claims seem to be similar to descriptive claims: To say that an act is right seems to be a matter of making an assertion, thus indicating that the speaker has a moral belief about which she can be correct or mistaken. On the other hand, moral claims seem to be different from descriptive claims: There is a sense in which, by claiming that an act is right, a speaker indicates (...) that she is inclined to perform the act, to want others to perform it, and to react with praise towards those who do it. Hybrid theories maintain that utterances of moral sentences have both a descriptive and a practical linguistic function. In this thesis, I investigate how a hybrid theory can best accommodate the descriptive and the practical aspects of moral language. I evaluate and criticize the way that existing hybrid theories have proposed to explain the duality of moral language. The main arguments against these views are that they either: fail to accommodate the way that the practical or attitudinal import of moral claims vary across different contexts and linguistic environments; or that they fail to show how the practical or attitudinal import is reliably inferred by interlocutors in virtue of general communicative principles. I develop and defend a new hybrid theory called ‘dynamic descriptivism’. This theory accommodates the duality of moral language by appeal to the way that moral utterances affect a dimension of communication which consists of the shared assumptions that interlocutors mutually assume to mutually accept. Moreover, I discuss a problem which has affected a wide range of theories of moral language – including existing hybrid theories – which is the problem of explaining what it is that interlocutors disagree about when they disagree about matters of morality. I argue that that dynamic descriptivism offers new resources for solving this problem. (shrink)

Hybrid languages are expansions of propositional modal languages which can refer to worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work has focussed on a more constrained system called $\mathscr{H}$. We show in detail that $\mathscr{H}$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations and a syntactic characterization. The key result to emerge is that $\mathscr{H}$ corresponds to the fragment of first-order logic (...) which is invariant for generated submodels. We then show that $\mathscr{H}$ enjoys interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage $\mathscr{H}$. Finally, we provide complexity results for $\mathscr{H}$ and other fragments and variants, and sharpen known undecidability results for $\mathscr{H}$. (shrink)

This is an extended version of the lectures given during the 12-thConference on Applications of Logic in Philosophy and in the Foundationsof Mathematics in Szklarska Poręba. It contains a surveyof modal hybrid logic, one of the branches of contemporary modal logic. Inthe first part a variety of hybrid languages and logics is presented with adiscussion of expressivity matters. The second part is devoted to thoroughexposition of proof methods for hybrid logics. The main point is to showthat (...) application of hybrid logics may remarkably improve the situation inmodal proof theory. (shrink)

This essay characterizes the perception of the visual hybrid as nonconceptual, introducing the terminology of nonconceptual content theory to aesthetics. The visual hybrid possesses a radical but nonetheless exemplary aesthetic composition and is well established in culture, art, and even design. The essay supplies a philosophical analysis of the results of cross-cultural experiments, showing that while categorization or conceptual hierarchization kicks in when the visual hybrids are juxtaposed with linguistic descriptions, no conceptual scheme takes effect when participants are (...) presented with mere visual hybrids. In isolation, the hybrids do not lend themselves to classification. I draw four conclusions from these experimental outcomes: 1. The perception of visual hybrids follows the structure of a nonconceptual mental content, because the original categories or concepts of the hybrids’ components are not combined into one, and their properties are not applied to one another, therefore none of the components reconstructs the other such that it is introduced to a new category. 2. Language freezes the hybridity of the visual hybrid into conceptuality. 3. Given that language has a freezing effect in the case of an extreme visual phenomenon such as the hybrid, it is all the more restraining in moderate artistic compositions, such as visual metaphors, in which properties of one component (the source) are applied to the other (the target). In those, nonconceptuality emerges from relatively organized compositions, forms, and relations, and from the dependence of objects and their properties on perceptual context. 4. Thus, the nonconceptualist terminology is suitable for the analysis of aesthetic perception in general and aesthetic perception’s relation to language. Keywords aesthetics, perception, nonconceptual content, hybrids, visual metaphors. (shrink)

Non-adjacent or long-distance dependencies (LDDs) are routinely considered to be a distinctive trait of language, which purportedly locates it higher than other sequentially organized signal systems in terms of structural complexity. This paper argues that particular languages display specific resources (e.g. non-interpretive morphological agreement paradigms) that help the brain system responsible for dealing with LDDs to develop the capacity of acquiring and processing expressions with such a human-typical degree of computational complexity. Independently obtained naturalistic data is discussed and put (...) to the service of the idea that the above-mentioned resources exert their developmental role from the outside, but in compliance with other internal resources, ultimately compounding an integrated developmental system. Parallels with other human and nonhuman developmental phenomena are explored, which point to the conclusion that the developmental system of concern can be assimilated to cases currently been conceptualized as ‘cue-response systems’ or ‘developmental hybrids’ within the ecological-developmental paradigm in theoretical biology. Such a conclusion is used to support the idea that both current externalist and internalist concepts fall short of a correct characterization of language. (shrink)

In this paper we discuss two hybrid languages, ℒ and ℒ, and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to 'label' states by using A and ↓ to bind special state variables.This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to (...) blend the modal idea of canonical models with the classical idea of witnessed maximal consistent sets. The languages ℒ and ℒ provide us with two extreme examples of the issues involved. In the case of ℒ, we can combine these ideas relatively straightforwardly with the aid of analogs of the Barcan axioms coupled with a modal theory of labeling. In the case of ℒ, on the other hand, although we can still formulate a theory of labeling, the Barcan analogs are not valid. We show how to overcome this difficulty by using COV*, an infinite collection of additional rules of proof which has been used in a number of investigations of extended modal logic. (shrink)

The case law of the Court of Justice of the European Union is shaped by the language in which it is drafted—i.e. French. However, because French is rarely the mother tongue of those drafting that case law, the texts produced are often stilted and awkward. In addition, those drafting such case law are constrained in their use of language and style of writing. These factors have led to the development of a ‘Court French’ which necessarily shapes the case law produced (...) and has implications for its development, particularly insofar as it inevitably leads to a type of precedent in that case law. That case law also undergoes many permutations of translation into and out of up to 23 different languages. The resultant texts that make up the case law are hybrid in nature—consisting of a blend of cultural and linguistic patterns, constrained by a rigid formulistic drafting style and put through many permutations of translation. The present paper investigates the production of the Court’s multilingual case law and considers whether the hybrid nature of that case law can actually aid the presentation of a ‘uniform’ EU case law. (shrink)

This paper revisits two fundamental issues in question semantics—what does a question mean, and how is this meaning compositionally derived? Drawing on observations with the distribution of wh-words in questions and free relatives as well as quantificational variability effects in question-embeddings, I argue that the nominal meanings of short answers must be derivable from question denotations, which therefore calls for a categorial approach to defining questions, including embedded questions. I provide a novel hybrid categorial approach to compose questions. This (...) approach overcomes the problems with traditional categorial approaches in defining bare wh-indefinites, composing multi-wh questions, and accounting for coordinations of questions. (shrink)

A hybrid theory is any moral theory according to which different classes of individuals ought to be treated according to different principles. We argue that some hybrid theories are able to meet standards of psychological plausibility, by which we mean that it’s feasible for ordinary human beings to understand and act in accord with them. Insofar as psychological plausibility is a theoretical virtue, then, such hybrid theories deserve more serious consideration. To make the case for this view, (...) we explain what psychological plausibility is and why we might value it, why the human/animal divide appears to be an entrenched feature of human psychology, and why Robert Nozick’s hybrid theory doesn’t go far enough. Finally, we make the case that a more promising psychologically plausible hybrid theory, with respect to humans and animals, will be (at least) at tribrid theory—that is, positing three domains rather than two. (shrink)

The ‘European Green Deal’ (EGD) is a set of communications from the European Commission that outlines EU roadmap to climate neutrality by 2050. The policy envisions that, with the facilitation of speedy and just ‘green transition’, the goals of environmental protection and economic development can be reconciled. This article offers a language-focused critical study of the EGD. After giving an overview of neoliberal ‘discourses of sustainability’ and explaining the notion of ‘interdiscursivity’ in CDS, it presents the results of a close (...) thematic analysis supported by keyword and concordance analysis of representations of ‘environment’ and ‘climate’ on the one hand, and ‘economy’ and ‘transition’ on the other. This study attends to salient language patterns and reveals how interdiscursive crossovers are established to normalise ‘sustainability’ as the contingency between environmental and economic orders of discourse. Also, it identifies the discursive strategies of nomination, predication, argumentation, perspectivisation and mitigation or intensification and shows how tensions between discourses are smoothened. This analysis of EGD’s ideological hybridity also sheds light onto how EU institutions are (self)authorised to lead actions on environmental challenges on behalf of European citizens. (shrink)

In this paper, we draw on Foucault's and Deleuze's theorisations of discipline and control, respectively, to understand a teacher accountability system in the US state of Texas: the Texas Teacher Evaluation and Support System (hereafter, T-TESS). Specifically, we focus on the interplay of physical and virtual modes of governance – which we develop here as physical–virtual hybridity – and the techniques that make these physical and virtual domains compatible via language interoperability, with T-TESS deployed as a representative empirical case to (...) show how such technologies work to govern teacher subjectivity. First, in-person appraiser meetings and observations re-code teachers’ linguistic behaviours, so their physical bodies and practices can become legible to and interoperable with the hybrid T-TESS system. This avoids any possible syntax errors between the linguistic expression of physical teacher speech and the digital coding language of T-TESS. Second, these digital bodies of data can now be viewed as proxies for the physical teacher body in the classroom, allowing the constant modulation in physical space (teacher bodies) and digital space (bodies of data). This is the physical–virtual hybridity of T-TESS, whereby discipline and control work symbiotically to govern both the physical and the digital expressions of teachers and their teaching. In this way, the disciplining of teachers’ language has profound effects on teachers’ bodies, both corporeal and digital. (shrink)

Hybrid identities are sentences in a special second order language with identity. The model classes of sets of hybrid identities are called hybrid solid varieties. We give a Birkhoff-type-characterization of hybrid solid varieties and develop a hybrid equational logic.

We study hybrid logics in topological semantics. We prove that hybrid logics of separation axioms are complete with respect to certain classes of finite topological models. This characterisation allows us to obtain several further results. We prove that aforementioned logics are decidable and PSPACE-complete, the logics of T 1 and T 2 coincide, the logic of T 1 is complete with respect to two concrete structures: the Cantor space and the rational numbers.

The hybrid logic and the independence friendly modal logic IFML are compared for their expressive powers. We introduce a logic IFML c having a non-standard syntax and a compositional semantics; in terms of this logic a syntactic fragment of IFML is singled out, denoted IFML c . (In the Appendix it is shown that the game-theoretic semantics of IFML c coincides with the compositional semantics of IFML c .) The hybrid logic is proven to be strictly more expressive (...) than IFML c . By contrast, and the full IFML are shown to be incomparable for their expressive powers. Building on earlier research (Tulenheimo and Sevenster 2006), a PSPACE -decidable fragment of the undecidable logic is disclosed. This fragment is not translatable into the hybrid logic and has not been studied previously in connection with hybrid logics. In the Appendix IFML c is shown to lack the property of ‘quasi-positionality’ but proven to enjoy the weaker property of ‘ bounded quasi-positionality’. The latter fact provides from the IFML internal perspective an account of what makes the compositional semantics of IFML c possible. (shrink)

In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics.In this paper we analyze the complexity of (...) the satisfiability problem of a number of hybrid temporal logics: the basic hybrid language over transitive trees; nominal Until logic; and referential interval logic. We discuss the effects of including nominals, the @ operator, the somewhere modality E, and the difference operator D. Adding nominals to tense logic leads for several frame-classes to an increase in complexity of the satisfiability problem from PSPACE to EXPTIME. On transitive trees, however, the satisfiability problem for this language can be decided in PSPACE. Along the way we make a detour through hybrid propositional dynamic logic: we establish upper bounds for a number of temporal logics by generalizing results due to Passy and Tinchev [29] and De Giacomo [16]. We conclude with some remarks on the relevance of our results to description logic, and draw attention to the utility of the spypoint technique for proving upper and lower bounds. (shrink)

A common starting point for ‘going hybrid’ is the thought that moral discourse somehow combines belief and desire-like aspects, or is both descriptive and expressive. Hybrid meta-ethical theories aim to give an account of moral discourse that is sufficiently sensitive to both its cognitive and its affective, or descriptive and expressive, dimensions. They hold at least one of the following: moral thought: moral judgements have belief and desire-like aspects or elements; moral language: moral utterances both ascribe properties and (...) express desire-like attitudes. This entry concerns hybrid theories of moral language. The main division within such theories is between those treating the expression of desire-like attitudes as semantic and those treating it as pragmatic. This entry exclusively focuses on pragmatic forms of and examines the prospects for treating moral attitude expression as working via certain standard pragmatic mechanisms. I explain these mechanisms, outline the properties that standardly define them, and test to see whether moral attitude expression matches them. At the end, I briefly explain a more minimal pragmatic alternative. The main conclusions are that we should disregard presupposition and conventional implicature views and that the most plausible options for a pragmatic hybrid view are a generalised conversational implicature view and a more minimal pragmatic view. (shrink)

Contemporary hybrid logic is based on the idea of using formulas as terms, an idea invented and explored by Arthur Prior in the mid-1960s. But Prior’s own work on hybrid logic remains largely undiscussed. This is unfortunate, since hybridisation played a role that was both central to and problematic for his philosophical views on tense. In this paper I introduce hybrid logic from a contemporary perspective, and then examine the role it played in Prior’s work.

Today the movement of ideas, capital and people is faster and wilder than at any point in history. Globalization has made the world more interconnected. The flows of traffic in this new network have not only accelerated to new levels, but the directions of movement have multiplied and abandoned the well-worn paths. The cultural dynamics of globalization have presented new challenges to the existing models for explaining the forms of belonging and the patterns of exchange that are occurring in the (...) world. Culture is no longer understood as the discrete and unique expression of activities and ideas that occur in particular places. No culture can exist in isolation. The process of hybridization in the deterritorialization of cultures and peoples demands new theories of flow and resistance and is compelling artists and intellectuals to rethink their methods. Cultural critics and curators are also in need of new conceptual frameworks. There is an urgent need for a new vocabulary in art discourse that is able to make sense of the complex forms of representation that are incorporating images from different locations and that simultaneously activate signs that contain within them a multiplicity of other signs, each embodying a series of contrary or competing codes. To do justice to both the complexity of the artwork and the intellectual potential of these new conceptual headings we need to develop frameworks that can address both these signs of difference and the process by which signs are made out of the plays with difference. The concept of translation can serve as a tool that can both make sense of the broader dynamic of cultural exchange and explain specific forms of cultural representation. I am particularly concerned with the ways in which contemporary artists and art writing deal with issues of mobility and attachment. What sort of place does art connote if it is constantly evoking the shuttling between places? In what language can the artist articulate the recognition that translations fail as often as they succeed? How does a bi-lingual or a bi-cultural person speak their mother-tongue and see the world, which operates in a different or hybrid language? These questions push the available conceptual frameworks for cross-cultural exchanges to the limits. In this article I re-examine the conceptual viability of the term hybridity in light of the new debates on creolization and globalization. (shrink)

The main aim of the present paper is to use a proof system for hybrid modal logic to formalize what are called false-belief tasks in cognitive psychology, thereby investigating the interplay between cognition and logical reasoning about belief. We consider two different versions of the Smarties task, involving respectively a shift of perspective to another person and to another time. Our formalizations disclose that despite this difference, the two versions of the Smarties task have exactly the same underlying logical (...) structure. We also consider the Sally-Anne task, having a more complicated logical structure, presupposing a “principle of inertia” saying that a belief is preserved over time, unless there is belief to the contrary. (shrink)

A computer-based language system exploring hybrid invention generation has been developed by Bill Seaman working in conjunction with the programmer Gideon May.1 The project was primarily funded by Intel. This work explores 3D visualization with related generative texts and recombinant audio/music, as well as a series of textual descriptions. Computer-based environmental meaning is explored through the inter-authorship and operative experiential examination of a diverse set of media-elements and media-processes, in this case focusing on the virtual construction of hybrid (...) inventions. Differing sets of media elements in the Hybrid Invention Generator convey their own fields of meaning through the juxtaposition of 3D models, texts and digital audio. Varying combinations of these fields of meaning are experienced through direct interaction with the system. The work explores notions surrounding machinic genetics. Nonsense relations can present seemingly off-kilter juxtapositions, providing the participant with an experience akin to surrealism. Lautréamont’s definition of surrealist beauty - ‘beautiful as the unexpected meeting, on a dissection table, of a sewing machine and an umbrella’ (Waldberg 1965) - describes an experience engendered through a unique juxtaposition of elements not unlike relations encountered within this particular techno-poetic environment. Yet the system can also be used to brainstorm actual devices, as well as their potential conceptual/functional construction. (shrink)

Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...”, “it Has always been in the past...” and “it will always Going to be in the future...” respectively. Valuation of formulae built from these operators are carried out on Kripke semantics, so Modal Logic and Temporal Logic are consequently (...) related. In fact, Temporal Logic is an extension of Modal one. Even when both logics mechanisms are able to formalize modal-temporal information with some accuracy, they suffer from a lack of expressiveness which Hybrid Logic can solve. Indeed, one of the problems of Modal Logic consists in its incapacity of naming specific points inside a model. As Temporal Logic is based on it, it cannot make such a thing neither. But First-Order Logic does can by means of constants and equality relation. Hybrid Logic, which results from combining Modal Logic and First-Order Logic, may solve this shortcoming. The main aim of this paper is to explain how Hybrid Logic emanates from Modal and Temporal ones in order to show what it adds to both logics with regard to information representation, why it is more expressive than them and what relation it maintains with the First-Order Correspondence Language. (shrink)

Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...”, “it Has always been in the past...” and “it will always Going to be in the future...” respectively. Valuation of formulae built from these operators are carried out on Kripke semantics, so Modal Logic and Temporal Logic are consequently (...) related. In fact, Temporal Logic is an extension of Modal one. Even when both logics mechanisms are able to formalize modal-temporal information with some accuracy, they suffer from a lack of expressiveness which Hybrid Logic can solve. Indeed, one of the problems of Modal Logic consists in its incapacity of naming specific points inside a model. As Temporal Logic is based on it, it cannot make such a thing neither. But First-Order Logic does can by means of constants and equality relation. Hybrid Logic, which results from combining Modal Logic and First-Order Logic, may solve this shortcoming. The main aim of this paper is to explain how Hybrid Logic emanates from Modal and Temporal ones in order to show what it adds to both logics with regard to information representation, why it is more expressive than them and what relation it maintains with the First-Order Correspondence Language. (shrink)

This paper examines and classifies the computational complexity of model checking and satisfiability for hybrid logics over frames with equivalence relations. The considered languages contain all possible combinations of the downarrow binder, the existential binder, the satisfaction operator, and the global modality, ranging from the minimal hybrid language to very expressive languages. For model checking, we separate polynomial-time solvable from PSPACE-complete cases, and for satisfiability, we exhibit cases complete for NP, PS pace , NE xp T (...) ime , and even N2E xp T ime . Our analysis includes the versions of all these languages without atomic propositions, and also complete frames. (shrink)

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and first-order hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ (...) that rigidly returns the value that $\alpha_a$ receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic. (shrink)

We extend Moss and Parikh’s bi-modal system for knowledge and effort by means of hybrid logic. In this way, some additional concepts from topology related to knowledge can be captured. We prove the soundness and completeness as well as the decidability of the extended system. Special emphasis will be placed on algebras.

The purpose of this paper is to argue that the hybrid formalism fits naturally in the context of David Lewis’s counterfactual logic and that its introduction into this framework is desirable. This hybridization enables us to regard the inference “The pig is Mary; Mary is pregnant; therefore the pig is pregnant” as a process of updating local information (which depends on the given situation) by using global information (independent of the situation). Our hybridization also has the following technical advantages: (...) (i) it preserves the completeness and decidability of Lewis’s logic; (ii) it allows us to characterize the Limit Assumption as a proof-rule with some side-conditions; and (iii) it enables us to establish a general Kripke completeness result by using the proof-rule corresponding to the Limit Assumption. Keywords Counterfactual logic - David Lewis - Contextually definite description - Hybrid logic - Arthur Prior - The limit assumption - Strong completeness - Decidability - Bisimulation - Pure completeness. (shrink)

According to an influential account of the new mechanistic philosophy of science, entities and activities compose mechanisms. However, the new mechanists have paid too little attention to activities. Critics have charged that accounts of activities in the new mechanism literature are philosophically uninformative and opaque. This paper defends a novel account of causally productive activities, which I call the Hybrid Account, that marries the two dominant philosophical approaches to causation: production and difference-making. The Hybrid Account of Activities (HAA) (...) identifies causally productive activities as robust difference-makers to the next stage of a mechanism. The Hybrid Account provides attractive solutions to causal identification and causal selection problems faced by earlier activities views. (shrink)

Does the English demonstrative pronoun 'that' (including complex demonstratives of the form 'that F') have sense and reference? Unlike many other philosophers of language, Frege answers with a resounding 'No'. He held that the bearer of sense and reference is a so-called 'hybrid proper name' (Künne) that contains the demonstrative pronoun and specific circumstances of utterance such as glances and acts of pointing. In this paper I provide arguments for the thesis that demonstratives are hybrid proper names. After (...) outlining why Frege held the hybrid proper name view, I will defend it against recent criticism, and argue that it is superior to views that take demonstrative pronouns to be the bearer of semantic properties. (shrink)

In this paper, I present main ideas of the Hybrid Theory of Reference for Proper Names. First, I try to define the ​position of the Hybrid Theory within the discussion about reference. Then I briefly explain most significant aspects of the theory as they were defined by Gareth Evans. Apart from that, I also offer some additions to the theory. The addition, I spend most space on concerns phrases that I call “mock names” which are expressions that look (...) like proper names but in fact are nothing more than abbreviations for descriptions used attributively. (shrink)

Provided we agree about the thing, it is needless to dispute about the terms. —David Hume, A treatise of human nature, Book 1, section VIIMap-like representations are frequently invoked as an alternative type of representational vehicle to a language of thought. This view presupposes that map-systems and languages form legitimate natural kinds of cognitive representational systems. I argue that they do not, because the collections of features that might be taken as characteristic of maps or languages do not (...) themselves provide scientifically useful information above and beyond what the individual features provide. To bring this out, I sketch several allegedly distinctive features of maps, and show how they can easily be grafted onto a simple logical language, resulting in a hybrid “manguage.” The ease with which these linguistic and map-like properties can be integrated into a single representational system raises the question of what work broader categories like language and map are doing. I maintain that, as an empirical matter of fact, they serve no particular purpose in cognitive science, and thus do not characterize distinct kinds of cognitive architectures. (shrink)

Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order (...) functional calculus and Completeness in propositional type theory. More precisely, from and we take the idea of building the model described by the maximal consistent set; in our case the maximal consistent set has to be named, \-saturated and extensionally algebraic-saturated due to the hybrid and equational nature of \. From, we use the result that any element in the hierarchy has a name. The challenge was to deal with all the heterogeneous components in an integrated system. (shrink)

Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order (...) functional calculus and Completeness in propositional type theory. More precisely, from and we take the idea of building the model described by the maximal consistent set; in our case the maximal consistent set has to be named, \-saturated and extensionally algebraic-saturated due to the hybrid and equational nature of \. From, we use the result that any element in the hierarchy has a name. The challenge was to deal with all the heterogeneous components in an integrated system. (shrink)

In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which (...) extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic. (shrink)

I examine two sets of experimental results about the semantics of general terms, by Genone and Lombrozo (2012) and by Nichols, Pinillos and Mallon (forthcoming) that allegedly reveal significant variations in semantic intuitions as regards the correct application of general terms. The two sets of authors propose two entirely different semantic treatments: Genone and Lombrozo espouse a hybrid semantics whereas Nichols, Pinillos and Mallon are inclined towards an appeal to ambiguity. I cast some doubts on the coherence of a (...) hybrid theory and argue in favor of the ambiguity approach. But I also argue that the sort of ambiguitiy Nichols, Pinillos and Mallon postulate is easy to incorporate to non-descriptivist approaches. (shrink)

This paper contributes to the principled construction of tableau-based decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For converse-free formulas we present a terminating control that does not rely on the usual chain-based blocking scheme. Our tableau systems are based on a new model existence theorem.

Prior's approach to time has been neglected by semanticists for several reasons. The main one, we believe, is the inability of Priorean tense logic to refer to times. The second one, is the inability to account for some important features of natural language such as temporal anaphora and the role of temporal constructions in discourse. Priorean tense logic has, however, one important advantage over other accounts: the internal perspective of time (due to its modal nature). This paper examines extensions of (...) Priorean tense logic in which reference to times is possible, focusing on the so-called hybrid temporal logic. We will outline some of its main features and analyze some of its philosophical implications. (shrink)

We show that basic hybridization makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$@_i$\end{document} in propositional and first-order hybrid logic. This means: interpret \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$@_i\alpha _a$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha _a$\end{document} is an expression of any type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document}, as an expression of type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document} that rigidly returns the value that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha_a$\end{document} receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic. (shrink)

We show that the bounded fragment of first-order logic and the hybrid language with and operators are equally expressive even with polyadic modalities, but that their fragments are equally expressive only for unary modalities.