Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories T₁, T₂ intersecting in a totally categorical sub-theory T₀. We show that if, e.g., T₀ is the theory of infinite vector spaces over a finite field then the fusion theory Tω exists, is complete and ω-stable of rank ω. We give a detailed geometrical analysis of Tω, proving that if both T₁, T₂ are 1-based then, Tω can be collapsed into a strongly minimal theory, if some (...) additional technical conditions hold—all trivially satisfied if T₀ is the theory of infinite vector spaces over a finite field Fq. (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)

The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain: applying it to finite sublanguages and taking the pointwise limit of the resulting probabilities as the size n of the sublanguage (...) increases; selecting a probability function on the language as a whole whose entropy on finite sublanguages of size n is not dominated by that of any other probability function for sufficiently large n. The entropy-limit conjecture says that, where these two approaches yield determinate probabilities, the two methods yield the same probabilities. If this conjecture is found to be true, it would provide a boost to the project of seeking a single canonical inductive logic—a project which faltered when Carnap's attempts in this direction succeeded only in determining a continuum of inductive methods. The truth of the conjecture would also boost the project of providing a canonical characterisation of normal or default models of first-order theories. Hitherto, the entropy-limit conjecture has been verified for languages which contain only unary predicate symbols and also for the case in which the constraints can be captured by a categorical statement of quantifier complexity. This paper shows that the entropy-limit conjecture also holds for categorical statements of complexity, for various non-categorical constraints, and in certain other general situations. (shrink)

In this paper I consider the question of whether absolute discernibility is attainable in symmetric languages. Simon Saunders has proven that all facts expressible in first-order language with identity can be equivalently stated within its symmetric sublanguage. I use this result to show specifically how particles of the same type can be absolutely discerned in the permutation-invariant language of the quantum theory of many particles.

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems (...) and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. (shrink)

Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of theorems with much wider (...) scope of applicability. In particular, we show how many of these fragments are really distinct and we find axiomatic systems for most of them. In fact, we construct strongly separable axiomatic systems for eight of our nine logics. We also fully answer the question for which of the studied fragments the corresponding class of algebras forms a variety. Finally, we solve the problem how to axiomatize predicate versions of logics without the lattice disjunction. (shrink)

The systems T N and T M show that necessity can be consistently construed as a predicate of syntactical objects, if the expressive/deductive power of the system is deliberately engineered to reflect the power of the original object language operator. The system T N relies on salient limitations on the expressive power of the language L N through the construction of a quotational hierarchy, while the system T Mrelies on limiting the scope of the modal axioms schemas to the sublanguage (...) L infM +, which corresponds exactly with the restrictive hierarchy of L N. The fact that L infM + is identical to the image of the metalinguistic mapping C + from the normal operator system into L M reveals that iterated operator modality is implicitly hierarchical, and that inconsistency is produced by applying the principles of the modal logic to formulas which have no natural analogues in the operator development. Thus the contradiction discovered by Montague can be diagnosed as the result of instantiating the axiom schemas with modally ungrounded formulas, and thereby adding radically new modal axioms to the predicate system.The predicate treatment of necessity differs significantly from that of the operator in that the cumulative models for the predicate system are strictly first-order. Possible worlds are not used as model-theoretic primitives, but rather alternate models are appealed to in order to specify the extension of N, which is semantically construed as a first-order predicate. In this manner, the intensional aspects of modality are built into the mode of specifying the particular set of objects which the denotation function assigns to N, rather than in the specification of the basic truth conditions for modal formulas. Intensional phenomena are thereby localised to the special requirements for determining the extension of a particular predicate, and this does not constitute a structural modification of the first-order models, but rather limits the relevant class of models to those which possess an appropriate denotation function. (shrink)

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems (...) and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. (shrink)

Let T be a simple L-theory and let \ be a reduct of T to a sublanguage \ of L. For variables x, we call an \-invariant set \\) in \ a universal transducer if for every formula \\in L^-\) and every a, $$\begin{aligned} \phi ^-\ L^-\text{-forks } \text{ over }\ \emptyset \ \text{ iff } \Gamma \wedge \phi ^-\ L\text{-forks } \text{ over }\ \emptyset. \end{aligned}$$We show that there is a greatest universal transducer \ and it is type-definable. In (...) particular, the forking topology on \\) refines the forking topology on \\) for all y. Moreover, we describe the set of universal transducers in terms of certain topology on the Stone space and show that \ is the unique universal transducer that is \-type-definable with parameters. If \ is a theory with the wnfcp and T is the theory of its lovely pairs of models we show that \\) and give a more precise description of the set of universal transducers for the special case where \ has the nfcp. (shrink)

We use a deontic logic of collective agency to study reducibility questions about collective agency and collective obligations. The logic that is at the basis of our study is a multi-modal logic in the tradition of *stit* logics of agency. Our full formal language has constants for collective and individual deontic admissibility, modalities for collective and individual agency, and modalities for collective and individual obligations. We classify its twenty-seven sublanguages in terms of their expressive power. This classification enables us to (...) investigate reducibility relations between collective deontic admissibility, collective agency, and collective obligations, on the one hand, and individual deontic admissibility, individual agency, and individual obligations, on the other. (shrink)

We present a procedure which allows us to recover classical and nonclassical logical structures as concrete logics associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for a given theory ${{\mathcal{T}}}$ and classical language ${{\fancyscript{L}}}$ expressing ${{\mathcal{T}}, }$ an observative sublanguage L of ${{\fancyscript{L}}}$ with a notion of truth as correspondence, introducing in L a derived and theory-dependent notion of C-truth (true with certainty), defining a physical preorder $\prec$ induced by C-truth, and finally selecting (...) a set of sentences ϕ V that are verifiable (or testable) according to ${{\mathcal{T}}, }$ on which a weak complementation ⊥ is induced by ${{\mathcal{T}}. }$ The triple $(\phi_{V},\prec,^{\perp})$ is then the desired concrete logic. By applying this procedure we recover a classical logic and a standard quantum logic as concrete logics associated with classical and quantum mechanics, respectively. The latter result is obtained in a purely formal way, but it can be provided with a physical meaning by adopting a recent interpretation of quantum mechanics that reinterprets quantum probabilities as conditional on detection rather than absolute. Hence quantum logic can be considered as a mathematical structure formalizing the properties of the notion of verification in quantum physics. This conclusion supports the general idea that some nonclassical logics can coexist without conflicting with classical logic (global pluralism) because they formalize metalinguistic notions that do not coincide with the notion of truth as correspondence but are not alternative to it either. (shrink)

In the article the issue of singling out some systemic criteria of differentiation between the fundamental and applied terminologies is considered. The authors point at the fact that each terminology has its own individual peculiarities, which mark it out against a general background of the terminological fund of a certain language. It is asserted that one of the most important and effective criteria that can be the basis of the approach to the study of sublanguages for special purposes is a (...) fundamental or applied character of the sphere of professional or scientific knowledge verbalized by a certain terminology. Such terms, as ‘fundamental terminology‘, ‘applied terminology‘ and ‘terminology of transition type‘, are introduced for scientific use. The fundamental terminology is understood as a sublanguage for special purposes that verbalizes the notions, forming the totality of fundamental knowledge, serving for the description of phenomena and processes in reality and in science, in the framework of which the fundamental research is carried out. The applied terminology is the name for the sublanguage for special purposes representing the notions, in which the results of human being’s practical scientific-industrial activity for changing the reality, forming the artificial habitat, are conceptualized. The terminology of transition type is the terminology that verbalizes the fragments of the field of scientific knowledge in which the research can have both a fundamental and applied character. The authors come to the conclusion that pure applied or fundamental terminologies are quite rare, that it is rational to speak about the degree of manifestation of the applied or fundamental character within the limits of this or that terminological system. (shrink)

We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} and a sublanguage L of the language of the formula, we can decide whether \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} has a uniform interpolant with respect to L in K4. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free case is proved using a reduction to the Gödel Löb Logic GL, while in the general case we prove that the question of whether a modal formula has uniform interpolants over transitive frames can be reduced to a decidable expressivity problem on the μ-calculus. (shrink)

We argue that the simplicity condition on a probability function on sentences of a predicate language L that it takes only finitely many values on the sentences of any finite sublanguage of L can be viewed as rational. We then go on to investigate consequences of this condition, linking it to the model theoretic notion of quantifier elimination.

Körner's notion of vagueness, its relation to ostension and the alledged gulf between logic and experience are examined. Ostension is seen not to cause vagueness ~ there are precise concepts of mathematics which can be ostensively mtroduced. A distinction is drawn between classical logic not applymg to the vague world and not applymg to the vague language. The claims about logic and the vague world are unverifiable claims about existence. Körner's attempt to elimmate the seeming incompatibility between vague language and (...) logic leads to a Protagorean relativism which is rejected. It is denied that the incompatibility between vagueness and classical logic causes a gulf between two sublanguages; mstead, ordinary language is held to contam both and so to be inconsistent. (shrink)

Problems of functional style differentiation of modern literary language are considered and analyzed in the article. Taking into account the communicative and pragmatic function, various substyles and sublanguages formed as a result of practical language usage in society are singled out on the example of the scientific style.

The application of the maximum entropy principle to determine probabilities on finite domains is well-understood. Its application to infinite domains still lacks a well-studied comprehensive approach. There are two different strategies for applying the maximum entropy principle on first-order predicate languages: applying it to finite sublanguages and taking a limit; comparing finite entropies of probability functions defined on the language as a whole. The entropy-limit conjecture roughly says that these two strategies result in the same probabilities. While the conjecture is (...) known to hold for monadic languages as well as for premiss sentences containing only existential or only universal quantifiers, its status for premiss sentences of greater quantifier complexity is, in general, unknown. I here show that the first approach fails to provide a sensible answer for some \-premiss sentences. I discuss implications of this failure for the first strategy and consequences for the entropy-limit conjecture. (shrink)

The application of the maximum entropy principle to determine probabilities on finite domains is well-understood. Its application to infinite domains still lacks a well-studied comprehensive approach. There are two different strategies for applying the maximum entropy principle on first-order predicate languages: applying it to finite sublanguages and taking a limit; comparing finite entropies of probability functions defined on the language as a whole. The entropy-limit conjecture roughly says that these two strategies result in the same probabilities. While the conjecture is (...) known to hold for monadic languages as well as for premiss sentences containing only existential or only universal quantifiers, its status for premiss sentences of greater quantifier complexity is, in general, unknown. I here show that the first approach fails to provide a sensible answer for some \-premiss sentences. I discuss implications of this failure for the first strategy and consequences for the entropy-limit conjecture. (shrink)

Popper's methodology does not entail any playing down of the various indispensible distinctions such as the distinction between knowing and guessing, the distinction between myth and science, the distinction between the observational and the theoretical, and between the vernacular and technical sublanguages or technical vocabulary. By avoiding both the totalization that led to the foundationalist position and the scepticist reactions to these frustrated foundationalist hopes, Popper's methodology makes it possible to combine fallibilism with a realist view of theories. It combines (...) the perennial willingness to re-examine positions, statements, etc. with the claim that a particular theory (as an item of knowledge in the objective sense) constitutes cognitive progress over its rivals. However, some of his formulations have been deliberately provocative and in this way have given rise to certain misgivings about possible paradoxical implications, even in philosophers congenial with Popper's approach. The concept of knowledge in the objective sense is, of course, an explicatum which Popper proposes primarily for use in methodology and epistemology. The concept is an expression of the acknowledgment of fallibility in principle. The phrasing that ‘knowledge is conjectural’ or ‘knowledge is fallible’, even when it refers to knowledge in the objective sense, is but an abbreviation for: since our methods for ascertaining the truth-value of a particular statement about empirical reality are fallible in principle, there cannot be any certain knowledge about reality. In everyday life and in politics tolerance will be possible to the extent to which the recognition of this fallibility is more than a declaration. (shrink)

The purpose of this paper is to explicit the possible extension of Speech Act theory to the analysis of sublanguages or Languages for Special Purposes , and to show in particular its relevance to the subset known as English for Special Purposes . I will primarily introduce an outline of LSP-ESP and of the Speech Act theory: then, through a survey on relevant literature, the modalities whereby Speech Acts could be made useful for English for Specific Purposes and, in so (...) doing, I will attempt to make their applicability to ESP explicit and theory-informed, in order to reach a synthesis. (shrink)

Feigl is concerned with the problem of how one sublanguage supplants another, e.g., how the language of quantum mechanics may be said to supplant that of classical physics. As a preliminary to tackling the problem, it has first to be generalized. Thus, in order to indicate how one language might supplant another, the line of a general theory of truth has to be traced. Among the conditions that such a theory has to satisfy is that its truth criteria must permit (...) us to evaluate current consensus judgments in science as true, on a par with the truth of our everyday ‘factual’ or ‘noninferential’ judgments. (shrink)

The determination of the meaning of theoretical terms by the axioms of theories as meaning postulates and the merely fictitious character of a basic observational language leads to Feyerabends problem of the incommensurability of physical theories. Different theories are actually compared by physicists as well. They might have a common sublanguage as the language of macroscopic physics in atomic physics. Furthermore shared metalaws (e. g. invariance principles) define an equivalence relation which identifies terms of different theories and enables physicists to (...) talk about them in a common language. (shrink)

The monograph shows that in the last 50 years theoretical linguistics remains a compendium of mutually contradicting doctrines on multiple levels: the level of general theories of language, the level of its main constituents (the lexicon, syntax, and the lexical-syntactic interface that connects them), and the lower levels of specific linguistic problems (such as lexical polysemy, grammatical meanings, etc.). The contradictions of contemporary linguistic theories are indicative of a deep crisis. Evolutionary-synthetic theory of language is aimed at overcoming this crisis. (...) It implements a multidisciplinary approach that describes the language a) in evolutionary and ontogenetic development and b) in close interaction with other human subsystems: the mental representation of the world, human activity and social interaction. Language is defined as a dual system developing in ontogeny: 'universal sensory sublanguage + ethnically specific functional sublanguage' where the sensory sublanguage is used to describe the 'visible' world (accessible to the senses), and the functional sublanguage is employed to describe the conceivable world ('comprehended by human mind'). Within the framework of the approach presented, many problems are solved: 1) the cognitive (non-verbal) language for representing language meanings; 2) diversity and unity of languages (using the structure alternative to Chomsky's Universal Grammar); 3) the main (original) function of the language; 4) the cognitive language of thought (its basis is the lexical and grammatical meanings of the sensory sublanguage); 5) dual (functionally prototypical) structure of human categories; 6) mechanisms in the early acquisition of lexical and grammatical meanings; 7) the meaning (assignment) of the syntactic structure of a sentence, etc. The book deals with a wide range of issues related to human cognition, glottogenesis and anthropogenesis, universal cognitive structures for the representation of objects, actions and situations, so it will be of interest not only to linguists, but also to psychologists, anthropologists, sociologists, philosophers. (shrink)

The article considers the issue of legal discourse evolution in the context of today’s civilization informatization in the postmodern era and intercultural dialogue which determines the understanding of fundamental judicial notions relative to the consciousness of an individual as a subject of legal and economic operations, as well as an implementer of social-economic and cultural rights. Given that the Internet environment in the 21st century is characterized by hypertextual discourse, this raises the matter of differentiation between objective and axiological scientific (...) knowledge contributing to a deeper understanding of the universe. The principles of further research in different scientific fields in the context of their social and socialization role in the information society are perceived as the coevolutionary basis of the informational civilization. Also noteworthy is the functional structural analysis of terms’ extraction from the symbolization of the language system, the prospective analysis of legal terms’ functioning, the study of their formal and semantic structure, the classification of legal sublanguage terms and the adjustment, unification and standardization of the term-based system. (shrink)

Körner's notion of vagueness, its relation to ostension and the alledged gulf between logic and experience are examined. Ostension is seen not to cause vagueness ~ there are precise concepts of mathematics which can be ostensively introduced. A distinction is drawn between classical logic not applying to the vague world and not applying to the vague language. The claims about logic and the vague world are unverifiable claims about existence. Körner's attempt to elimmate the seeming incompatibility between vague language and (...) logic leads to a Protagorean relativism which is rejected. It is denied that the incompatibility between vagueness and classical logic causes a gulf between two sublanguages; instead, ordinary language is held to contain both and so to be inconsistent. (shrink)

In order to avoid the use of individual variables in predicate calculus, several authors proposed language whose expressions can be interpreted, in general, as denotations of predicates . The present author also proposed a language of this kind [5]. The absence of individual variables makes all these languages rather different from the traditional language of predicate calculus and from the usual language of mathematics. The translation procedures from the ordinary predicate languages into the predicate languages without individual variables and vice (...) versa have a technical character. It is desirable to make possible carrying out such procedures by performing some transformations in a suitable new language which comprises both a sublanguage similar to the ordinary predicate languages and another one not using individual variables. We shall propose now a language of the desired kind. The expressions of this language could be interpreted, in general, as denoting predicates which depend on parameters on a given object domain – this predicate has one argument and depends on one parameter). The proposed language will have the modal features noted in [3] and [5]. It is worthy of mention that the language proposed at the end of [4] although containing expressions interpreted as predicates and expressions with parameters does not allow simultaneous availability of argument places and parameters. (shrink)

Popper's methodology does not entail any playing down of the various indispensible distinctions such as the distinction between knowing and guessing, the distinction between myth and science, the distinction between the observational and the theoretical, and between the vernacular and technical sublanguages or technical vocabulary. By avoiding both the totalization that led to the foundationalist position and the scepticist reactions to these frustrated foundationalist hopes, Popper's methodology makes it possible to combine fallibilism with a realist view of theories. It combines (...) the perennial willingness to re-examine positions, statements, etc. with the claim that a particular theory (as an item of knowledge in the objective sense) constitutes cognitive progress over its rivals. However, some of his formulations have been deliberately provocative and in this way have given rise to certain misgivings about possible paradoxical implications, even in philosophers congenial with Popper's approach. The concept of knowledge in the objective sense is, of course, an explicatum which Popper proposes primarily for use in methodology and epistemology. The concept is an expression of the acknowledgment of fallibility in principle. The phrasing that ‘knowledge is conjectural’ or ‘knowledge is fallible’, even when it refers to knowledge in the objective sense, is but an abbreviation for: since our methods for ascertaining the truth-value of a particular statement about empirical reality are fallible in principle, there cannot be any certain knowledge about reality. In everyday life and in politics tolerance will be possible to the extent to which the recognition of this fallibility is more than a declaration. (shrink)