Anglistik (Subject) / Semantics (Lesson)

Grundlagen der Semantic

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• What does it mean to "understand" a sentence? To understand a sentence means to be able to say whether the sentence - describes an aspect of the world as it is (i.e. describes a state of affairs) or - does not describe an aspect of the world as it is (i.e. does not describe a state of affairs) OR to know what the world would have to be like for the sentence to describe a state of affairs
• What is the difference between "Object-level" and "Meta-level"? Object-level: "talking in expressions"e.g. Paul is a student   Meta-level: "talking about expressions"e.g. "Paul is a student" is a declarative sentence
• What is a "contingent" truth? Give an example A contingent truth is true because the world is as it is. The morning star is the evening star = true, because morning star and evening star are two expressions for the same planet, namely Venus
• What is a "tautological" truth? Give an example A tautological truth is true because of the form of the sentence. The morning star is the morning star this cannot ever be false.
• How do the expressions "the morning star" and "the evening star" equal and differ? They equal each other with respect to the designated object. => they both talk about the same thing!They have the same reference! They differ from each other with respect to the way this object is identified. => they talk about the same object but use different names!They have a different sense!
• Explain the terms "reference" and "sense" Sense: the way in which references are identified Reference: the denotation of an expression (sth. outside the language) The sense is like a function  that determines a reference for some expression:sense(expression) = reference The sense establishes the relation between the expression to which it is connected and the reference of the expression.
• What is the reference of a name? an individual
• What is the reference of a declarative sentence? a truth value
• What is the reference of a property? a set of individuals / entities
• What is the reference of a relational expression relating two individuals? E.g.: "hits", as in "Paul hits Bob" a set of pairs of individuals
• What is the relation of a relational expression relating three entities? E.g.: "hands", like in "Paul hand Bob the book" a set of triples of entities / individuals
• What is the reference of a DP? E.g.: "the book", like in "Paul read the book" an entity (under certain conditions)
• Why is the reference of a DP an entity only under certain conditions? syntactically similar DPs can have entirely different interpretations: a) Paul is a studentb) a student is someone who is enrolled at a universityc) a student entered the room in a) "being a student" is a property of Paulin b) "a student" doesn´t denote an individual either, the sentence would be just as good if there were no students at allin c) "a student" actually denotes an individual that has entered the room DPs that actually stand for individuals are called referential
• What is a referential DP? A DP that actually stand for an individual
• What is the reference of a noun? E.g.: "book" in "Paul reads a book" a set of individuals / entities
• Quote the Principle of Compositionality The interpretation of a complex expression is a function of the interpretation of its constituent expressions
• What does a well-formed expression consist of? (Rules of Syntax) (1) exactly one propositional symbol in the minimal case or (2)a) one 1-place operator followed by a well-formed expressionb) one 2-place operator follwed by two well-formed expressionsc) a well-formed expression with surrounding brackets  
• What is the task of the interpretation function? to map propositions to truth values
• What is the domain and the range of the interpretation function? domain:the set of (simple and complex) propositions range:the set of truth values {t, f}
• 1-place operators are interpreted as functions that map... truth values to truth values
• 2-place operators are interpreted as functions that map ... pairs of truth values to truth values (makes sense, it takes two propositions (=two truth values) as an input and spits out one truth value  
• Which is the only 1-place operator and what does it do? the negation operator, it turns the input value around t becomes f f becomes t
• What are the four 2-place operators we use? andt + t = tt + f = ff + t = ff + f = f = only if both inputs are t the output is t ort + t = tt + f = tf + t = tf + f = f only if both inputs a f the output is f if - thent + t = tt + f = ff + t = tf + f = t ex falso quodlibet= from a false premise anything can be concluded if and only if - then t + t = tt + f = ff + t = ff + f = t
• In which case are two propositions equivalent? iff they are equivaltent under all circumstances, i.e. iff they choose the same truth value options in every case!
• In which chase are two operators equivalent? iff they define the same output values on the basis of identical input values.
• When is a complex proposition a tautology? iff it is interpreted as t for every truth value assignment of its constituent propositions. => true because of the form of the expression and not because of the input values
• When is a complex proposition a contradiction? iff it is interpreted as f for every truth value assignment of its constituent propositions. => false because of its form and not because of the input values
• What is a "logical truth" a tautology, which is true because of its form
• What is a "logical antonomy"? a contradiction, which false because of its form
• What is "modus ponens"? an inference (schlussfolgernde) pattern: All X are Y Z is an X = Z is a Y
• Give a natural language example of modus ponens! All men are mortal Socrates is a man = Socrates is mortal
• What are the "Rules of Syntax" in Predicate Logic? a well-formed expression, i.e. a proposition, minimally consists of:(1) one predicate symbol, followed by a pair of brackets, which surrounds exactly as many individual symbols (separated by commas) as the arity of the predicate symbol requiresP(a), Q(x, y) ... Non-minimally consists of:(2)a) a 1-place operator followed by a well-formed expressionb) a 2-place operator between two well-formed expressions (3) a quantifier symbol followed by an individual variable followed by a well-formed expression (4)a) a well-formed expression with surrounding bracketsb) a propositional symbol used as a abbreviation for a proposition
• What are the implementations of n-place predicate terms? The reference of a 1-place predicate term is a set of individuals 2-place predicate term is a set of pairs of individuals 3-place predicate term is a set of triples of individuals 4-place predicate term is a set of quadruples of individuals ...
• What are the domains and ranges of the more complex interpretation function in Predicate Logic? Domains:- propositional terms- predicate terms (with different arity)- individual terms Ranges:- truth values- sets of (different arrangements of) individuals- individuals
• What is the "universe of discourse, D"? also called an ontology = a list of individuals "that are there" for the interpretation function to pick from
• What is the difference between minimal and non-minimal expressions? minimal = simple non-minimal = complex
• what consists the model M of? F = the interpretation function and D = the universe of discourse
• Why are there no lexical statements for individual variables? variables are supposed to not always refer to the same individual. They are supposed to be able to refer to different individuals if need be They are more like pronouns:"she" doesnt always refer to Paula, in a different context it might just as well refer to Louisa.
• What is g? A function for the assignment of values to individual variables. g does not belong to the model. It is a mechanical means of assigning each individual variable exactly one individual from D
• Explain the difference between the universal and the existential quantifier! Universal quantifier = checks everything in the universe of discourse= for the expression "everybody is a student" to be true, every individual of D needs to be in fact a student! Existential quantifier = claims the existence of at least one= for the expression "at least one is a student" to be true, at least one individual in D needs to be a student.If there are more - fineif not - fine as well as long as one is a student
• What is "scope"? the domain of application, meaning the proposition(s) to which a quantifier applies. To avoid ambiguities the scope is marked with brackets.
• What are possible worlds? - each alternative assignment of values to predicate terms in a model is called a possible world - the distinguished assignment (the one we use) is called the "actual" or "real" world
• What are simplex expressions? expressions that we would not account for compositionally. The semantics of simplex expressions is often also called "lexical semantics"
• What is the task of the semantics of simplex expressions? semantic inquiry into simplex expressions (i.e. lexical items) must identify and semantically describe lexical knowledge about these items.
• What are "accidental" and "not accidental" relations? Accidental:e.g. the relation between "smokers" and "men"> the relation could easily be different if the real world were different>> synthetic proposition Not accidental:e.g. the relation between "men" and "humans"> this relation is rooted in the language system, in no possible world could the relation be such as that men are not humans>> analytic proposition

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