Argument Structure and the Syntax-Morphology Interface. a Case Study in Latin and Other Languages

Total Page:16

File Type:pdf, Size:1020Kb

Argument Structure and the Syntax-Morphology Interface. a Case Study in Latin and Other Languages Argument structure and the syntax-morphology interface. A case study in Latin and other languages Víctor Acedo Matellán ADVERTIMENT. La consulta d’aquesta tesi queda condicionada a l’acceptació de les següents condicions d'ús: La difusió d’aquesta tesi per mitjà del servei TDX (www.tdx.cat) ha estat autoritzada pels titulars dels drets de propietat intel·lectual únicament per a usos privats emmarcats en activitats d’investigació i docència. No s’autoritza la seva reproducció amb finalitats de lucre ni la seva difusió i posada a disposició des d’un lloc aliè al servei TDX. No s’autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant al resum de presentació de la tesi com als seus continguts. En la utilització o cita de parts de la tesi és obligat indicar el nom de la persona autora. ADVERTENCIA. La consulta de esta tesis queda condicionada a la aceptación de las siguientes condiciones de uso: La difusión de esta tesis por medio del servicio TDR (www.tdx.cat) ha sido autorizada por los titulares de los derechos de propiedad intelectual únicamente para usos privados enmarcados en actividades de investigación y docencia. No se autoriza su reproducción con finalidades de lucro ni su difusión y puesta a disposición desde un sitio ajeno al servicio TDR. No se autoriza la presentación de su contenido en una ventana o marco ajeno a TDR (framing). Esta reserva de derechos afecta tanto al resumen de presentación de la tesis como a sus contenidos. En la utilización o cita de partes de la tesis es obligado indicar el nombre de la persona autora. WARNING. On having consulted this thesis you’re accepting the following use conditions: Spreading this thesis by the TDX (www.tdx.cat) service has been authorized by the titular of the intellectual property rights only for private uses placed in investigation and teaching activities. Reproduction with lucrative aims is not authorized neither its spreading and availability from a site foreign to the TDX service. Introducing its content in a window or frame foreign to the TDX service is not authorized (framing). This rights affect to the presentation summary of the thesis as well as to its contents. In the using or citation of parts of the thesis it’s obliged to indicate the name of the author. Argument structure and the syntax-morphology interface. A case study in Latin and other languages Víctor Acedo Matellán PhD thesis Supervisor: Dr Jaume Mateu Fontanals Tutor: Dr Joana Rosselló Ximenes Doctorat en Lingüística i Comunicació, bienni 2000-2002 Departament de Lingüística General Facultat de Filologia Universitat de Barcelona December 2010 2 Table of contents TABLE OF CONTENTS..................................................................................................3 ACKNOWLEDGEMENTS...............................................................................................7 LIST OF ABBREVIATIONS...........................................................................................9 CHAPTER 1 INTRODUCTION AND LAYOUT......................................................13 1 Aim and proposal ................................................................................................... 13 2 Methodology ........................................................................................................... 14 2.1 The advantages of a theoretical approach to the grammar of unspoken languages 14 2.2 Data and corpus ...........................................................................................................15 3 Layout of the dissertation...................................................................................... 16 CHAPTER 2 A NEO-CONSTRUCTIONIST PERSPECTIVE ON ARGUMENT STRUCTURE.................................................................................................................19 1 Endo-skeletal versus exo-skeletal approaches to the lexicon-syntax interface. 19 1.1 Properties of the lexical item vs. properties of the structure ...................................19 1.2 A fuzzy frontier: Hale and Keyser, Levin and Rappaport Hovav ..........................24 1.2.1 Hale & Keyser’s theory of lexical syntax...............................................................25 1.2.2 Levin and Rappaport Hovav’s Event Structure Templates ....................................31 1.3 Constructionism and neo-constructionism................................................................32 1.4 Summary.......................................................................................................................37 2 Three neo-constructionist frameworks ................................................................ 37 2.1 Mateu 2002 ...................................................................................................................38 2.1.1 Semantic construal and conceptual content ............................................................38 2.1.2 Argument structure configurations .........................................................................38 2.1.3 Adjectives as non-basic categories .........................................................................39 2.2 Borer 2005b ..................................................................................................................43 2.2.1 Listemes and functional structure. Coercion ..........................................................43 2.2.2 Range assignment to functional categories.............................................................44 2.2.3 Event structure with arguments: range assignment through specifier-head relations 45 2.2.4 Event structure without arguments .........................................................................47 2.3 Distributed Morphology..............................................................................................49 2.3.1 A single generative engine. The Narrow Lexicon ..................................................49 2.3.2 The Vocabulary.......................................................................................................50 2.3.3 Semantic interpretation. The Encyclopaedia ..........................................................51 2.3.4 Operations along the PF-branch .............................................................................52 2.4 Summary.......................................................................................................................53 3 The present framework ......................................................................................... 53 3.1 Argument structure is syntax .....................................................................................54 3.1.1 No l-/s-syntax distinction........................................................................................54 3.1.2 Relational and non-relational elements...................................................................54 3 3.1.3 Argument structure configurations .........................................................................55 3.1.4 Adjunction of roots to functional heads..................................................................57 3.1.5 A small note on case ...............................................................................................59 3.2 The semantics of argument structure: a localist-aspectual approach ....................60 3.2.1 Structural and encyclopaedic semantics .................................................................60 3.2.2 Interpretation of functional heads and arguments...................................................60 3.2.3 Against root ontologies...........................................................................................64 3.2.4 Aspect and argument structure ...............................................................................64 3.2.4.1 Two-component theory of aspect..................................................................................64 3.2.4.2 The computation of situation aspect .............................................................................66 3.2.5 Phase theory and semantic interpretation: locality domains for special meaning ..69 3.3 The syntax-morphophonology interface....................................................................70 3.3.1 Words and structure. Cross-linguistic variation .....................................................70 3.3.2 Vocabulary insertion. Non-uniform insertion.........................................................72 3.3.3 Conflation ...............................................................................................................73 3.3.4 Affixation................................................................................................................77 3.3.5 Operations affecting nodes before Vocabulary Insertion: Lowering and Fusion...78 3.3.6 A cartography of the PF-branch: the timing of morphophonological operations...79 3.4 Summary.......................................................................................................................82 4 Overall summary.................................................................................................... 82 CHAPTER 3 LATIN AS A SATELLITE-FRAMED LANGUAGE........................85 1 Talmy’s (2000) theory of change events and its adaptation to the present framework ..................................................................................................................... 86 1.1 Talmy’s theory of (motion) events..............................................................................86
Recommended publications
  • CAS LX 522 Syntax I
    It is likely… CAS LX 522 IP This satisfies the EPP in Syntax I both clauses. The main DPj I′ clause has Mary in SpecIP. Mary The embedded clause has Vi+I VP is the trace in SpecIP. V AP Week 14b. PRO and control ti This specific instance of A- A IP movement, where we move a likely subject from an embedded DP I′ clause to a higher clause is tj generally called subject raising. I VP to leave Reluctance to leave Reluctance to leave Now, consider: Reluctant has two θ-roles to assign. Mary is reluctant to leave. One to the one feeling the reluctance (Experiencer) One to the proposition about which the reluctance holds (Proposition) This looks very similar to Mary is likely to leave. Can we draw the same kind of tree for it? Leave has one θ-role to assign. To the one doing the leaving (Agent). How many θ-roles does reluctant assign? In Mary is reluctant to leave, what θ-role does Mary get? IP Reluctance to leave Reluctance… DPi I′ Mary Vj+I VP In Mary is reluctant to leave, is V AP Mary is doing the leaving, gets Agent t Mary is reluctant to leave. j t from leave. i A′ Reluctant assigns its θ- Mary is showing the reluctance, gets θ roles within AP as A θ IP Experiencer from reluctant. required, Mary moves reluctant up to SpecIP in the main I′ clause by Spellout. ? And we have a problem: I vP But what gets the θ-role to Mary appears to be getting two θ-roles, from leave, and what v′ in violation of the θ-criterion.
    [Show full text]
  • Syntax and Semantics of Propositional Logic
    INTRODUCTIONTOLOGIC Lecture 2 Syntax and Semantics of Propositional Logic. Dr. James Studd Logic is the beginning of wisdom. Thomas Aquinas Outline 1 Syntax vs Semantics. 2 Syntax of L1. 3 Semantics of L1. 4 Truth-table methods. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun. ‘likes logic’ is a verb phrase. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. ‘Bertrand Russell’ is a proper noun. ‘likes logic’ is a verb phrase. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘likes logic’ is a verb phrase. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun. ‘likes logic’ is a verb phrase. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun.
    [Show full text]
  • Syntax: Recursion, Conjunction, and Constituency
    Syntax: Recursion, Conjunction, and Constituency Course Readings Recursion Syntax: Conjunction Recursion, Conjunction, and Constituency Tests Auxiliary Verbs Constituency . Syntax: Course Readings Recursion, Conjunction, and Constituency Course Readings Recursion Conjunction Constituency Tests The following readings have been posted to the Moodle Auxiliary Verbs course site: I Language Files: Chapter 5 (pp. 204-215, 216-220) I Language Instinct: Chapter 4 (pp. 74-99) . Syntax: An Interesting Property of our PS Rules Recursion, Conjunction, and Our Current PS Rules: Constituency S ! f NP , CP g VP NP ! (D) (A*) N (CP) (PP*) Course Readings VP ! V (NP) f (NP) (CP) g (PP*) Recursion PP ! P (NP) Conjunction CP ! C S Constituency Tests Auxiliary Verbs An Interesting Feature of These Rules: As we saw last time, these rules allow sentences to contain other sentences. I A sentence must have a VP in it. I A VP can have a CP in it. I A CP must have an S in it. Syntax: An Interesting Property of our PS Rules Recursion, Conjunction, and Our Current PS Rules: Constituency S ! f NP , CP g VP NP ! (D) (A*) N (CP) (PP*) Course Readings VP ! V (NP) f (NP) (CP) g (PP*) Recursion ! PP P (NP) Conjunction CP ! C S Constituency Tests Auxiliary Verbs An Interesting Feature of These Rules: As we saw last time, these rules allow sentences to contain other sentences. S NP VP N V CP Dave thinks C S that . he. is. cool. Syntax: An Interesting Property of our PS Rules Recursion, Conjunction, and Our Current PS Rules: Constituency S ! f NP , CP g VP NP ! (D) (A*) N (CP) (PP*) Course Readings VP ! V (NP) f (NP) (CP) g (PP*) Recursion PP ! P (NP) Conjunction CP ! CS Constituency Tests Auxiliary Verbs Another Interesting Feature of These Rules: These rules also allow noun phrases to contain other noun phrases.
    [Show full text]
  • Interview with Noam Chomsky
    INTERVIEW WITH NOAM CHOMSKY Alessandro Boechat de Medeiros1 Avram Noam Chomsky is a world-renowned linguist, philosopher and political activist. He is Professor Emeritus in the Department of Linguistics at Massachusetts Institute of Technology and recently became a laureate Professor in the Department of Linguistics at University of Arizona. He has been the leader of the generative enterprise in linguistic theory since its beginning, in the late fifties, and is considered by many the father of modern Linguistics. In fact, his views have influenced the whole field and established points of departure for research in formal syntax, phonology and even semantics. Born in Philadelphia, in 1928, Chomsky started his undergraduate studies in Philosophy and Linguistics at the University of Philadelphia, in 1945. He concluded his Ph.D. in Linguistics in 1955, under the supervision of Zellig Harris, at the same University, with the thesis The Logical Structure of Linguistic Theory, a revolutionary work only published in 1975. Two years later, in 1957, he published Syntactic Structures (SS), one of his most famous linguistics books, considered by many a true revolution in the field. SS was in part based on The Logical Structure of Linguistic Theory, and exerted a great influence during late fifties and early sixties among language scholars, defining to a great extent linguistics research developed in the years to come. In 1959 he published his famous review of B. F. Skinner’s book Verbal Behavior. The review presents a frontal and exhaustive critique of the behaviorist theory in a general way and also focally regarding language. Chomsky had other defining theoretical debates with Philosopher Michel Foucault2 and with Psychologist Jean Piaget3.
    [Show full text]
  • Lecture 1: Propositional Logic
    Lecture 1: Propositional Logic Syntax Semantics Truth tables Implications and Equivalences Valid and Invalid arguments Normal forms Davis-Putnam Algorithm 1 Atomic propositions and logical connectives An atomic proposition is a statement or assertion that must be true or false. Examples of atomic propositions are: “5 is a prime” and “program terminates”. Propositional formulas are constructed from atomic propositions by using logical connectives. Connectives false true not and or conditional (implies) biconditional (equivalent) A typical propositional formula is The truth value of a propositional formula can be calculated from the truth values of the atomic propositions it contains. 2 Well-formed propositional formulas The well-formed formulas of propositional logic are obtained by using the construction rules below: An atomic proposition is a well-formed formula. If is a well-formed formula, then so is . If and are well-formed formulas, then so are , , , and . If is a well-formed formula, then so is . Alternatively, can use Backus-Naur Form (BNF) : formula ::= Atomic Proposition formula formula formula formula formula formula formula formula formula formula 3 Truth functions The truth of a propositional formula is a function of the truth values of the atomic propositions it contains. A truth assignment is a mapping that associates a truth value with each of the atomic propositions . Let be a truth assignment for . If we identify with false and with true, we can easily determine the truth value of under . The other logical connectives can be handled in a similar manner. Truth functions are sometimes called Boolean functions. 4 Truth tables for basic logical connectives A truth table shows whether a propositional formula is true or false for each possible truth assignment.
    [Show full text]
  • 1 Logic, Language and Meaning 2 Syntax and Semantics of Predicate
    Semantics and Pragmatics 2 Winter 2011 University of Chicago Handout 1 1 Logic, language and meaning • A formal system is a set of primitives, some statements about the primitives (axioms), and some method of deriving further statements about the primitives from the axioms. • Predicate logic (calculus) is a formal system consisting of: 1. A syntax defining the expressions of a language. 2. A set of axioms (formulae of the language assumed to be true) 3. A set of rules of inference for deriving further formulas from the axioms. • We use this formal system as a tool for analyzing relevant aspects of the meanings of natural languages. • A formal system is a syntactic object, a set of expressions and rules of combination and derivation. However, we can talk about the relation between this system and the models that can be used to interpret it, i.e. to assign extra-linguistic entities as the meanings of expressions. • Logic is useful when it is possible to translate natural languages into a logical language, thereby learning about the properties of natural language meaning from the properties of the things that can act as meanings for a logical language. 2 Syntax and semantics of Predicate Logic 2.1 The vocabulary of Predicate Logic 1. Individual constants: fd; n; j; :::g 2. Individual variables: fx; y; z; :::g The individual variables and constants are the terms. 3. Predicate constants: fP; Q; R; :::g Each predicate has a fixed and finite number of ar- guments called its arity or valence. As we will see, this corresponds closely to argument positions for natural language predicates.
    [Show full text]
  • Lambda Calculus and the Decision Problem
    Lambda Calculus and the Decision Problem William Gunther November 8, 2010 Abstract In 1928, Alonzo Church formalized the λ-calculus, which was an attempt at providing a foundation for mathematics. At the heart of this system was the idea of function abstraction and application. In this talk, I will outline the early history and motivation for λ-calculus, especially in recursion theory. I will discuss the basic syntax and the primary rule: β-reduction. Then I will discuss how one would represent certain structures (numbers, pairs, boolean values) in this system. This will lead into some theorems about fixed points which will allow us have some fun and (if there is time) to supply a negative answer to Hilbert's Entscheidungsproblem: is there an effective way to give a yes or no answer to any mathematical statement. 1 History In 1928 Alonzo Church began work on his system. There were two goals of this system: to investigate the notion of 'function' and to create a powerful logical system sufficient for the foundation of mathematics. His main logical system was later (1935) found to be inconsistent by his students Stephen Kleene and J.B.Rosser, but the 'pure' system was proven consistent in 1936 with the Church-Rosser Theorem (which more details about will be discussed later). An application of λ-calculus is in the area of computability theory. There are three main notions of com- putability: Hebrand-G¨odel-Kleenerecursive functions, Turing Machines, and λ-definable functions. Church's Thesis (1935) states that λ-definable functions are exactly the functions that can be “effectively computed," in an intuitive way.
    [Show full text]
  • A Logical Approach to Grammar Description Lionel Clément, Jérôme Kirman, Sylvain Salvati
    A logical approach to grammar description Lionel Clément, Jérôme Kirman, Sylvain Salvati To cite this version: Lionel Clément, Jérôme Kirman, Sylvain Salvati. A logical approach to grammar description. Jour- nal of Language Modelling, Institute of Computer Science, Polish Academy of Sciences, Poland, 2015, Special issue on High-level methodologies for grammar engineering, 3 (1), pp. 87-143 10.15398/jlm.v3i1.94. hal-01251222 HAL Id: hal-01251222 https://hal.archives-ouvertes.fr/hal-01251222 Submitted on 19 Jan 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A logical approach to grammar description Lionel Clément, Jérôme Kirman, and Sylvain Salvati Université de Bordeaux LaBRI France abstract In the tradition of Model Theoretic Syntax, we propose a logical ap- Keywords: proach to the description of grammars. We combine in one formal- grammar ism several tools that are used throughout computer science for their description, logic, power of abstraction: logic and lambda calculus. We propose then a Finite State high-level formalism for describing mildly context sensitive grammars Automata, and their semantic interpretation. As we rely on the correspondence logical between logic and finite state automata, our method combines con- transduction, ciseness with effectivity.
    [Show full text]
  • FOL Syntax: You Will Be Expected to Know
    First-Order Logic A: Syntax CS271P, Fall Quarter, 2018 Introduction to Artificial Intelligence Prof. Richard Lathrop Read Beforehand: R&N 8, 9.1-9.2, 9.5.1-9.5.5 Common Sense Reasoning Example, adapted from Lenat You are told: John drove to the grocery store and bought a pound of noodles, a pound of ground beef, and two pounds of tomatoes. • Is John 3 years old? • Is John a child? • What will John do with the purchases? • Did John have any money? • Does John have less money after going to the store? • Did John buy at least two tomatoes? • Were the tomatoes made in the supermarket? • Did John buy any meat? • Is John a vegetarian? • Will the tomatoes fit in John’s car? • Can Propositional Logic support these inferences? Outline for First-Order Logic (FOL, also called FOPC) • Propositional Logic is Useful --- but Limited Expressive Power • First Order Predicate Calculus (FOPC), or First Order Logic (FOL). – FOPC has expanded expressive power, though still limited. • New Ontology – The world consists of OBJECTS. – OBJECTS have PROPERTIES, RELATIONS, and FUNCTIONS. • New Syntax – Constants, Predicates, Functions, Properties, Quantifiers. • New Semantics – Meaning of new syntax. • Unification and Inference in FOL • Knowledge engineering in FOL FOL Syntax: You will be expected to know • FOPC syntax – Syntax: Sentences, predicate symbols, function symbols, constant symbols, variables, quantifiers • De Morgan’s rules for quantifiers – connections between ∀ and ∃ • Nested quantifiers – Difference between “∀ x ∃ y P(x, y)” and “∃ x ∀ y P(x, y)”
    [Show full text]
  • On Synthetic Undecidability in Coq, with an Application to the Entscheidungsproblem
    On Synthetic Undecidability in Coq, with an Application to the Entscheidungsproblem Yannick Forster Dominik Kirst Gert Smolka Saarland University Saarland University Saarland University Saarbrücken, Germany Saarbrücken, Germany Saarbrücken, Germany [email protected] [email protected] [email protected] Abstract like decidability, enumerability, and reductions are avail- We formalise the computational undecidability of validity, able without reference to a concrete model of computation satisfiability, and provability of first-order formulas follow- such as Turing machines, general recursive functions, or ing a synthetic approach based on the computation native the λ-calculus. For instance, representing a given decision to Coq’s constructive type theory. Concretely, we consider problem by a predicate p on a type X, a function f : X ! B Tarski and Kripke semantics as well as classical and intu- with 8x: p x $ f x = tt is a decision procedure, a function itionistic natural deduction systems and provide compact д : N ! X with 8x: p x $ ¹9n: д n = xº is an enumer- many-one reductions from the Post correspondence prob- ation, and a function h : X ! Y with 8x: p x $ q ¹h xº lem (PCP). Moreover, developing a basic framework for syn- for a predicate q on a type Y is a many-one reduction from thetic computability theory in Coq, we formalise standard p to q. Working formally with concrete models instead is results concerning decidability, enumerability, and reducibil- cumbersome, given that every defined procedure needs to ity without reference to a concrete model of computation. be shown representable by a concrete entity of the model.
    [Show full text]
  • Syntax and Logic Errors Teacher’S Notes
    Syntax and logic errors Teacher’s Notes Lesson Plan Length 60 mins Specification Link 2.1.7/p_q Candidates should be able to: Learning objective (a) describe syntax errors and logic errors which may occur while developing a program (b) understand and identify syntax and logic errors Time (min) Activity Further Notes 10 Explain that syntax errors are very common, not just when programming, but in everyday life. Using a projector, display the Interactive Starter greatful, you’re, their, CD’s, Activity and ask the students to suggest where the Although there is much discussion of five syntax errors are. Internet security. Stress that even though there are syntax errors, we can still interpret the meaning of the message but computers are not as accommodating and will reject anything that does not meet the rules of the language being used. 15 Watch the set of videos pausing to discuss the content. 5 Discuss the videos to assess learning. Ask questions such as: • What is a syntax error? A syntax error is an error in the source code of a program. Since computer programs must follow strict syntax to compile correctly, any aspects of the code that do not conform to the syntax of the • Can you list some common syntax errors? programming language will produce a syntax error. • Spelling mistakes • Missing out quotes • Missing out brackets • Using upper case characters in key words e.g. IF instead of if • Missing out a colon or semicolon at end of a statement • What is a logic (or logical error)? • Using tokens in the wrong order A logic error (or logical error) is a ‘bug’ or mistake in a program’s source code that results in incorrect or unexpected behaviour.
    [Show full text]
  • Symbolic Logic: Grammar, Semantics, Syntax
    Symbolic Logic: Grammar, Semantics, Syntax Logic aims to give a precise method or recipe for determining what follows from a given set of sentences. So we need precise definitions of `sentence' and `follows from.' 1. Grammar: What's a sentence? What are the rules that determine whether a string of symbols is a sentence, and when it is not? These rules are known as the grammar of a particular language. We have actually been operating with two different but very closely related grammars this term: a grammar for propositional logic and a grammar for first-order logic. The grammar for propositional logic (thus far) is simple: 1. There are an indefinite number of propositional variables, which we have been symbolizing as A; B; ::: and P; Q; :::; each of these is a sen- tence. ? is also a sentence. 2. If A; B are sentences, then: •:A is a sentence, • A ^ B is a sentence, and • A _ B is a sentence. 3. Nothing else is a sentence: anything that is neither a member of 1, nor constructable via successive applications of 2 to the members of 1, is not a sentence. The grammar for first-order logic (thus far) is more complex. 2 and 3 remain exactly the same as above, but 1 must be replaced by some- thing more complex. First, a list of all predicates (e.g. Tet or SameShape) and proper names (e.g. max; b) of a particular language L must be specified. Then we can define: 1F OL. A series of symbols s is an atomic sentence = s is an n-place predicate followed by an ordered sequence of n proper names.
    [Show full text]