Philosophy of Language: Wittgenstein
... 1. For Russell, some singular terms are (genuine) names, i.e., expressions whose meaning in a proposition is just to refer to an object. Russell, however, denies Frege’s claim that all singular terms are names. Rather, some singular terms are definite descriptions. Examples of definite descriptions ...
... 1. For Russell, some singular terms are (genuine) names, i.e., expressions whose meaning in a proposition is just to refer to an object. Russell, however, denies Frege’s claim that all singular terms are names. Rather, some singular terms are definite descriptions. Examples of definite descriptions ...
Chapter One {Word doc}
... It is important to realize that one of the difficulties in translating back and forth from English (or any other natural language) to symbolic logic comes from the fact that some expressions are used in more than one way, logically speaking. In addition it is difficult to disambiguate because closel ...
... It is important to realize that one of the difficulties in translating back and forth from English (or any other natural language) to symbolic logic comes from the fact that some expressions are used in more than one way, logically speaking. In addition it is difficult to disambiguate because closel ...
An Introduction to Lower Bounds on Formula
... properties of Kripke frames and models. To put things in perspective, I am going to start by giving an informal overview of some techniques used for proving lower bounds on the size of Boolean formulae and then I am going to show how to extend and apply them in the modal case where we have obtained ...
... properties of Kripke frames and models. To put things in perspective, I am going to start by giving an informal overview of some techniques used for proving lower bounds on the size of Boolean formulae and then I am going to show how to extend and apply them in the modal case where we have obtained ...
the theory of form logic - University College Freiburg
... denies that there is an objectual identity relation at all: “That identity is not a relation between objects is obvious” (1922, §5.5301). He elaborates: “Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say not ...
... denies that there is an objectual identity relation at all: “That identity is not a relation between objects is obvious” (1922, §5.5301). He elaborates: “Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say not ...
Document
... one person is honest and always tells the truth one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
... one person is honest and always tells the truth one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
the common rules of binary connectives are finitely based
... information (for instance, if no information is at hand which of a given sample S of connectives was meant in a message from outside). The system may work provisorically with the rules common to all f ∈ S. That these are f.b. is particularly convenient for logical programming. ...
... information (for instance, if no information is at hand which of a given sample S of connectives was meant in a message from outside). The system may work provisorically with the rules common to all f ∈ S. That these are f.b. is particularly convenient for logical programming. ...
The semantics of predicate logic
... Readings: Section 2.4, 2.5, 2.6. In this module, we will precisely define the semantic interpretation of formulas in our predicate logic. In propositional logic, every formula had a fixed, finite number of models (interpretations); this is not the case in predicate logic. As a consequence, we must t ...
... Readings: Section 2.4, 2.5, 2.6. In this module, we will precisely define the semantic interpretation of formulas in our predicate logic. In propositional logic, every formula had a fixed, finite number of models (interpretations); this is not the case in predicate logic. As a consequence, we must t ...
Deductive Reasoning
... whoever was in the kitchen stole the tomatoes • Sherlock Holmes discovers that Mrs. Hudson was in the kitchen • What can he conclude? ...
... whoever was in the kitchen stole the tomatoes • Sherlock Holmes discovers that Mrs. Hudson was in the kitchen • What can he conclude? ...
Notes on Propositional and Predicate Logic
... An or- expression having a set of literals as its argument set is called a clause in the resolution method. After the described transformations one has a set of clauses as the premises, and a single clause as the desired conclusion, and this is the starting point for constructing a proof. One single ...
... An or- expression having a set of literals as its argument set is called a clause in the resolution method. After the described transformations one has a set of clauses as the premises, and a single clause as the desired conclusion, and this is the starting point for constructing a proof. One single ...
Math 2283 - Introduction to Logic
... If two sentences are accepted as true, of which one has the form of an implication while the other is the antecedent of this implication, then that sentence may also be recognized as true, which forms the consequent of the implication. (We detach thus, so to speak, the antecedent from the whole impl ...
... If two sentences are accepted as true, of which one has the form of an implication while the other is the antecedent of this implication, then that sentence may also be recognized as true, which forms the consequent of the implication. (We detach thus, so to speak, the antecedent from the whole impl ...
Review - Gerry O nolan
... proposition (46f). Hume could no more consistently advocate the sceptical thesis than he could the proposition 'All ravens are black.' It follows from the necessity of such assessments that there could never be some contingent presupposition, such as the uniformity of nature (23), the long run succe ...
... proposition (46f). Hume could no more consistently advocate the sceptical thesis than he could the proposition 'All ravens are black.' It follows from the necessity of such assessments that there could never be some contingent presupposition, such as the uniformity of nature (23), the long run succe ...
Computer Science 202a Homework #2, due in class
... Please turn in your homework in TWO SEPARATE PARTS: Part I is problems 1-3 and Part II is problems 4-6. Put your name on both parts. Please list (in Part I) any persons (including course staff) or resources (including online) you consulted with in connection with this assignment. Partial credit will ...
... Please turn in your homework in TWO SEPARATE PARTS: Part I is problems 1-3 and Part II is problems 4-6. Put your name on both parts. Please list (in Part I) any persons (including course staff) or resources (including online) you consulted with in connection with this assignment. Partial credit will ...
Monadic Predicate Logic is Decidable
... • Base Cases: G is atomic. G is of the form Pi(t) or of the form t1=t2 (t, t1, and t2 are variables or constants) 1. Let G = Pi(t). We need to prove: Pi(t) is satisfied by d1 in M iff Pi(t) is satisfied by e1 in M’ But d1 and e1 are similar, hence the same predicates hold true of d1 and e1 (includin ...
... • Base Cases: G is atomic. G is of the form Pi(t) or of the form t1=t2 (t, t1, and t2 are variables or constants) 1. Let G = Pi(t). We need to prove: Pi(t) is satisfied by d1 in M iff Pi(t) is satisfied by e1 in M’ But d1 and e1 are similar, hence the same predicates hold true of d1 and e1 (includin ...
( (ϕ ∧ ψ) - EEE Canvas
... system for propositional logic is a natural deduction system. In this kind of system, there is an “introduction” rule for each connective and an “elimination” rule for each connective. For instance, the introduction rule for “and” might say: if you can deduce ϕ and if you can deduce ψ, then you can ...
... system for propositional logic is a natural deduction system. In this kind of system, there is an “introduction” rule for each connective and an “elimination” rule for each connective. For instance, the introduction rule for “and” might say: if you can deduce ϕ and if you can deduce ψ, then you can ...
slides - National Taiwan University
... |= is about semantics, rather than syntax For Σ = ∅, we have ∅ |= τ , simply written |= τ . It says every truth assignment satisfies τ . In this case, τ is a tautology. ...
... |= is about semantics, rather than syntax For Σ = ∅, we have ∅ |= τ , simply written |= τ . It says every truth assignment satisfies τ . In this case, τ is a tautology. ...
Document
... An interpretation gives meaning to the nonlogical symbols of the language. An assignment of facts to atomic wffs a fact is taken to be either true or false about the world thus, by providing an interpretation, we also provide the truth value of each of the atoms ...
... An interpretation gives meaning to the nonlogical symbols of the language. An assignment of facts to atomic wffs a fact is taken to be either true or false about the world thus, by providing an interpretation, we also provide the truth value of each of the atoms ...
notes
... Let P be a propositions containing the (distinct) atomic formulas A 1 , . . . , An and v1 , . . . v2n its interpretations. We denote with v P the boolean function associated with P , i.e. vP : {0, 1}n → {0, 1} is defined as follows: for each (a 1 , . . . , an ), ai ∈ {0, 1}, there exists i ∈ {1, . ...
... Let P be a propositions containing the (distinct) atomic formulas A 1 , . . . , An and v1 , . . . v2n its interpretations. We denote with v P the boolean function associated with P , i.e. vP : {0, 1}n → {0, 1} is defined as follows: for each (a 1 , . . . , an ), ai ∈ {0, 1}, there exists i ∈ {1, . ...
A HIGHER-ORDER FINE-GRAINED LOGIC FOR INTENSIONAL
... Pollard (1999). With the exception of Turner (1992), these theories have focused on the interpretative structures while remaining inexplicit or programmatic about the logic. We depart from this tradition by constructing an explicit proof theory for a finegrained logic and then defining a class of mo ...
... Pollard (1999). With the exception of Turner (1992), these theories have focused on the interpretative structures while remaining inexplicit or programmatic about the logic. We depart from this tradition by constructing an explicit proof theory for a finegrained logic and then defining a class of mo ...