Quantification and Logical Form

O papel da lógica na filosofia é fundamentalmente metodológico já que é fazendo uso das diferentes estruturas de demonstração que teses filosóficas são estabelecidas. Por isso, no contexto da prática filosófica, a lógica deve ser tomada seu sentido mais largo, abarcando tanto a lógica formal quanto a informal. Dada a variação das formas de demonstração na filosofia e dado, portanto, o uso metodológico que a filosofia faz da lógica, argumento que, neste sentido, há uma continuidade entre os métodos formais e informais de demonstração. Para mostrar esta continuidade, partirei da noção fundamental de inferência lógica para estabelecer os critérios de diferenciação entre o formal e o informal, e reconstruirei brevemente a história filosófica da lógica para mostrar suas transformações e seu distanciamento progressivo do lugar metodológico na filosofia.Finalmente, considerando a literatura recente sobre lógica formal e informal, aponto os problemas relativos à suas diferenças e, partindo do reconhecimento de que lógica cumpre um papel metodológico na filosofia, argumento que a lógica formal e informal são práticas que estão em continuidade e se beneficiam mutuamente. No que diz respeito ao modo como a lógica informal se beneficia da lógica formal, o artigo investigará as vantagens e limitações em se tomar os sistemas de dedução natural como instrumento de análise de demonstrações em linguagem natural. No que diz respeito aos modos como a lógica formal pode se beneficiar da lógica informal, procuraremos mostrar que avanços na lógica formal decorrem, além dos esforços de formalização de provas informais, de uma análise informal das estratégias de cálculo e dos princípios segundos os quais uma certa linguagem lógica opera.

An E-Librarian Service allows users to enter complete questions in natural language (NL) in order to improve the retrieval capabilities (see section 1.3.3). The aim of the natural language processing (NLP) module of an E-Librarian Service is to translate a user question into a logical and computer-readable form. The more precise and accurate this translation is, the more complex the algorithm gets. In this chapter we present the necessary principles to design the NLP module of an E-Librarian Service that is able to “understand” the meaning of a user question and to translate it into a logical form.

The aim of this paper is to look into the Italian philosophy of religious language in order (1) to evaluate the reception of this discipline born in an analytic context and (2) to appreciate its original features. After an introduction which specifies the status of the philosophy of religious language, in the first paragraph three pioneering articles written between 1961 and 1966 are taken into consideration, because they determine the subsequent reception of this discipline. Then Bochenski’s, Ramsey’s and Ferre’s works translated into Italian are analyzed paying attention to the introductions that had launched the interpretation of their thesis. Micheletti’s and Antiseri’s historical reconstructions are considered in the third paragraph. They differ from one another in presenting the philosophy of religious language as the logical analysis of a particular type of speech or in the context of semantic atheism. The fourth paragraph is devoted to three ambits in which Italian philosophy of religious language is flourishing nowadays: biblical studies (through the linguistic status of metaphors), philosophy of prayer (through pragmatics) and formal logic (through formal ontology). In the light of these studies it is possible to conclude that the Italian philosophy of religious language is growing and that it is able to contribute to philosophy of religion and to interreligious dialogue in a relevant way

Corpora of child speech and child-directed speech (CDS) have enabled major contributions to the study of child language acquisition, yet semantic annotation for such corpora is still scarce and lacks a uniform standard. Semantic annotation of CDS is particularly important for understanding the nature of the input children receive and developing computational models of child language acquisition. For example, under the assumption that children are able to infer meaning representations for (at least some of) the utterances they hear, the acquisition task is to learn a grammar that can map novel adult utterances onto their corresponding meaning representations, in the face of noise and distraction by other contextually possible meanings. To study this problem and to develop computational models of it, we need corpora that provide both adult utterances and their meaning representations, ideally using annotation that is consistent across a range of languages in order to facilitate cross-linguistic comparative studies. This paper proposes a methodology for constructing such corpora of CDS paired with sentential logical forms, and uses this method to create two such corpora, in English and Hebrew. The approach enforces a cross-linguistically consistent representation, building on recent advances in dependency representation and semantic parsing. Specifically, the approach involves two steps. First, we annotate the corpora using the Universal Dependencies (UD) scheme for syntactic annotation, which has been developed to apply consistently to a wide variety of domains and typologically diverse languages. Next, we further annotate these data by applying an automatic method for transducing sentential logical forms (LFs) from UD structures. The UD and LF representations have complementary strengths: UD structures are language-neutral and support consistent and reliable annotation by multiple annotators, whereas LFs are neutral as to their syntactic derivation and transparently encode semantic relations. Using this approach, we provide syntactic and semantic annotation for two corpora from CHILDES: Brown’s Adam corpus (English; we annotate ≈ 80% of its child-directed utterances), all child-directed utterances from Berman’s Hagar corpus (Hebrew). We verify the quality of the UD annotation using an inter-annotator agreement study, and manually evaluate the transduced meaning representations. We then demonstrate the utility of the compiled corpora through (1) a longitudinal corpus study of the prevalence of different syntactic and semantic phenomena in the CDS, and (2) applying an existing computational model of language acquisition to the two corpora and briefly comparing the results across languages.

The article describes practice of using academic role-playing games at classes of Foreign Language in order to develop soft skills of students. Role-playing game is a means of developing soft skills, when observing such principles as: the use of a language as a complex system rather than a set of grammatical and lexical phenomena; the use of a language as a means of communication, and consequently, creating more content-centered than formal teaching and training materials, that are focused on communication; creating practice-oriented situations at classes, training not only subject knowledge and hard skills but social skills as well. The article presents a description of training materials, tasks, methods and forms of work.

In this Phd thesis,, we try to use formal logic and threshold phenomena that asymptotically emerge with certainty in order to build new trust models and to evaluate the existing one. The departure point of our work is that dynamic, global computing systems are not amenable to a static viewpoint of the trust concept, no matter how this concept is formalized. We believe that trust should be a statistical, asymptotic concept to be studied in the limit as the system's components grow according to some growth rate. Thus, our main goal is to define trust as an emerging system property that ``appears'' or disappears when a set of properties hold, asymptotically with probability$ 0$ or $1$ correspondingly . Here we try to combine first and second order logic in order to analyze the trust measures of specific network models. Moreover we can use formal logic in order to determine whether generic reliability trust models provide a method for deriving trust between peers/entities as the network's components grow. Our approach can be used in a wide range of applications, such as monitoring the behavior of peers, providing a measure of trust between them, assessing the level of reliability of peers in a network. Wireless sensor networks are comprised of a vast number of ultra-small autonomous computing, communication and sensing devices, with restricted energy and computing capabilities, that co-operate to accomplish a large sensing task. Sensor networks can be very useful in practice. Such systems should at least guarantee the confidentiality and integrity of the information reported to the controlling authorities regarding the realization of environmental events. Therefore, key establishment is critical for the protection in wireless sensor networks and the prevention of adversaries from attacking the network. Finally in this dissertation we also propose three distributed group key establishment protocols suitable for such energy constrained networks. This dissertation is composed of two parts. Part I develops the theory of the first and second order logic of graphs - their definition, and the analysis of their properties that are expressible in the {\em first order language} of graphs. In part II we introduce some new distributed group key establishment protocols suitable for sensor networks. Several key establishment schemes are derived and their performance is demonstrated.

The paper addresses the problem of generating sentences from logical formulae. It describes a simple and efficient algorithm for generating text which has been developed for use in machine translation, but will have wider application in natural language processing. An important property of the algorithm is that the logical form used to generate a sentence need not be one which could have been produced by parsing the sentence: formal equivalence between logical forms is allowed for. This is necessary for a machine translation system, such as the one envisaged in this paper, which uses single declarative grammars of individual languages, and declarative statements of translation equivalences for transfer. In such a system, it cannot be guaranteed that transfer will produce a logical form in the same order as would have been produced by parsing some target-language sentence, and it is not practicable to define a normal form for the logical forms. The algorithm is demonstrated using a categorial grammar and a simple indexed logic, as this allows a particularly clear and elegant formulation. It is shown that the algorithm can be adapted to phrase-structure grammars, and to more complex semantic representations than that used here.

Mixed inference machine reading comprehension method based on symbolic logic

This chapter deals with how to relate languages in this book to formal logics. The convention in the chapter is that a formal theory, or simply a theory, is a name for a set of formulas with no free variables in some formal logic. So how can you map (parts of) models to theories, and why should we do so? Relationships between requirements modeling languages and formal logics are a recurrent topic in requirements engineering. In KAOS, theories in linear temporal first-order logic are themselves parts of models. The same in Tropos. The motivation is that you can take a model in a requirements modeling language and map (parts of) it to a theory in some formal logic, in order to answer questions that your requirements modeling language could not. I will look at two among many topics on the relationships between requirements modeling languages and formal logics. I restrict the discussion to one formal logic, namely classical propositional logic (CPL), and discuss the following. 1. How to map a model to a CPL theory if every fragment equates to an atomic proposition. (Sect. 15.2) 2. How to map a model to CPL theory, if every fragment maps to a conjunction of formulas of classical propositional logic. (Sect. 15.3) 3. What can be the risks of mapping models to theories. (Sect. 15.4)

Traditional database query languages are based on set theory and crisp first order logic. However, many applications require retrieval-like queries which return result objects associated with a degree of being relevant to the query. Historically, retrieval systems estimate relevance by exploiting hidden object semantics whereas query processing in database systems relies on matching select-conditions with attribute values. Thus, different mechanisms were developed for database and information retrieval systems. In consequence, there is a lack of support for queries involving both retrieval and database search terms. In this work, we introduce the quantum query language (QQL). Its underlying unifying theory is based on the mathematical formalism of quantum mechanics and quantum logic. Van Rijsbergen already discussed the strong relation between the formalism of quantum mechanics and information retrieval. In this work, we interrelate concepts from database query processing to concepts from quantum mechanics and logic. As result, we obtain a common theory which allows us to incorporate seamlessly retrieval search into traditional database query processing.

In the two preceding papers ‘Completeness of Quantum Logic’ (CQL) and ‘Quantum Logical Calculi and Lattice Structures’ (QLC) an operational approach to formal quantum logic was developed. Beginning with a pragmatic definition of quantum mechanical propositions by means of material dialogs a formal dialog-game was introduced for establishing formally true propositions. It was shown in CQL that the formal dialog-game can be replaced by a calculus T eff of effective (intuitionistic) quantum logic which is complete and consistent with respect to the dialogic procedure. In QLC we showed that T eff is equivalent to a propositional calculus Q eff Since the calculus Q eff is a model for a certain lattice structure, called quasi-implicative lattice (L eff), the connection between quantum logic and the quantum theoretical formalism is provided. L qi is a weaker algebraic structure than the orthomodular lattice of the subspaces of a Hilbert space L q which can be interpreted as the pro-positional calculus of value-definite quantum logic. This establishes a quantum logical interpretation of L q.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.

In the language of symbolic logic a sentence or, as the logicians call it, a well-formed formula is constructed according to recursive rules. The idea that the rules of syntax of a language must be formulated recursively has been taken over by Chomsky and other transformational grammarians of natural languages. There is, accordingly, a kind of similarity between the procedure of sentence construction adopted by transformational grammarians and the corresponding procedure in symbolic logic - both are conceived of as recursive procedures. But there the similarity ends. To be sure, Chomsky maintains that the grammars of symbolic logic are incorporated in his approach - they are, he says, special instances of what he calls 'phrase structure grammars'. But is this contention true? Are the rules of syntax employed in symbolic logic really 'phrase structure grammars' in Chomsky's sense? In any case the application of the underlying principles to ordinary languages produces forms of grammar which deviate from Chomskyan 'phrase structure grammar' in a significant way. One thing I want to point out in this paper is this difference. However, once we have seen this difference we arrive at a way of looking at syntax which sheds new light on two important questions. One of these questions concerns the idea of 'transformations' as employed by the transformational grammarians. The other is the question of the connection between syntax and semantics.

During the past forty years the term "quantum logic" has been used with many different meanings and even today one has to distinguish between a large number of differing concepts of "quantum logic". A survey of the various interpretations of this expression can be found, for example, in the proceedings of a recent conference on "Current Issues in Quantum Logic".1 Due to this great ambiguity of the term "quantum logic" it seems necessary first to clarify what is meant precisely by "quantum logic" in this article. Here we consider a formal object language, the elementary pro positions of which are concerned with the present state and the temporal development of real physical objects. If this abstract language of physics describes objects that belong to that part of the physical reality which is governed by the laws of "classical physics" we call it C-language or 5^c. If, in addition, the language incorporates also propositions about physical objects which belong to the domain of "quantum physics", then this more universal language will be called O-language, or 6^0. The most abstract syntactical structure of this language 5^0, i.e., the formal logic of O-language, will be denoted as "quantum logic" or Q-logic. Analogously we call the formal logic of the more special language 6^c of classical physics C-logic. Whether the distinction between C-language and O-language and between C-logic and O-logic respectively is actually relevant will be discussed in the following sections. This explication of the term "quantum logic" leaves the question still open, whether this formal logic of quantum language can be justified by a priori reasons or whether it can be obtained solely from experience. Irrespective of the answer to this question, it is obvious that "quantum logic" represents some intrinsic structure of the physical reality which can be discovered at least in principle from physical observations or from a corresponding physical theory. Starting from the empirically well established quantum theory in Hilbert space, G. Birkhoff and J.v.

We study here equiformity, the standard identity criterion for sentences. This notion was put forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable but if the notion of sentence is taken as a fundamental basis for logic and mathematics, it seems that this principle cannot be maintained without vicious circle. It seems also that equiformity has some semantical features ; maybe this is not so clear for individual signs but sentences are often considered as meaningful combinations of signs. If meaning has to play a role, we are thus maybe in no better position than when dealing with identity criterion for propositions. In formal logic, one speaks rather about well-formed formulas, but closed formulas are called sentences because they are meaningful in the sense that they can be true or false. Formulas look better like mathematical objects than material inscriptions and equiformity does not seem to apply to them. Various congruencies can be considered as identities between formulas and in particular "to have the same logical form". One can say that the objects of study of logic are rather logical forms than sentences conceived as material inscriptions.