CSE 452: Programming Languages
... rather describe the form of the result It is assumed that the computer can determine how the result is to be obtained One needs to provide the computer with the relevant information and a method of inference for computing desirable results ...
... rather describe the form of the result It is assumed that the computer can determine how the result is to be obtained One needs to provide the computer with the relevant information and a method of inference for computing desirable results ...
CSE 452: Programming Languages
... form of the goal, with an object as its parameter, will cause X to be instantiated with that object’s value and this result displayed If there is no proposition with the form of the goal, the system indicates with a no that the goal can’t be satisfied Organization of Programming Languages-Cheng (F ...
... form of the goal, with an object as its parameter, will cause X to be instantiated with that object’s value and this result displayed If there is no proposition with the form of the goal, the system indicates with a no that the goal can’t be satisfied Organization of Programming Languages-Cheng (F ...
Remarks on Second-Order Consequence
... proofs from any premisses, free from the assumption of being true, let alone of being true as a matter of logic. In particular, we are interested in proofs in axiomatic theories. For this, what is needed is a systematizing not of logical truth, but rather of logical consequence. There are many deduc ...
... proofs from any premisses, free from the assumption of being true, let alone of being true as a matter of logic. In particular, we are interested in proofs in axiomatic theories. For this, what is needed is a systematizing not of logical truth, but rather of logical consequence. There are many deduc ...
Predicate Logic
... us to say that if certain things are true, certain other things are sure to be true, e.g. • X P(X) Q(X) P(something) ----------------- (so we can conclude) Q(something) • This involves matching P(X) against P(something) and binding the variable X to the ...
... us to say that if certain things are true, certain other things are sure to be true, e.g. • X P(X) Q(X) P(something) ----------------- (so we can conclude) Q(something) • This involves matching P(X) against P(something) and binding the variable X to the ...
Logical Argument
... the logical relationships between the premises, any intermediate assertions and the conclusion. The main logical property of an argument that is of concern to us here is whether it is truth preserving, that is if the premises are true, then so is the conclusion. We will usually abbreviate this prope ...
... the logical relationships between the premises, any intermediate assertions and the conclusion. The main logical property of an argument that is of concern to us here is whether it is truth preserving, that is if the premises are true, then so is the conclusion. We will usually abbreviate this prope ...
Introduction to logic
... We are going to deal with how to represent information in the KB and how to reason about it. We use logic as a device to pursue this aim. These notes are an introduction to modern logic, whose origin can be found in George Boole’s and Gottlob Frege’s works in the XIX century. However, logic in gener ...
... We are going to deal with how to represent information in the KB and how to reason about it. We use logic as a device to pursue this aim. These notes are an introduction to modern logic, whose origin can be found in George Boole’s and Gottlob Frege’s works in the XIX century. However, logic in gener ...
ch1_1
... are definitions: Two triangles are congruent if their vertices can be paired so that the corresponding sides are equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
... are definitions: Two triangles are congruent if their vertices can be paired so that the corresponding sides are equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
First-Order Logic, Second-Order Logic, and Completeness
... content cannot escape the rigorous logical form.19 This thought can certainly be found in the Begriffsschrift itself already. I take this thought to be of general importance: We are looking for formal systems which axiomatize, characterize, or formalize in some other way some notion, or notions, in s ...
... content cannot escape the rigorous logical form.19 This thought can certainly be found in the Begriffsschrift itself already. I take this thought to be of general importance: We are looking for formal systems which axiomatize, characterize, or formalize in some other way some notion, or notions, in s ...
p q
... •True if there is a y for which P(x,y) is true for every x. (i.e., true for a particular y regardless (or independent) of x) •False if for every y there is an x for which P(x,y) is false. Note that order matters here In particular, if yxP(x,y) is true, then xyP(x,y) is true. However, if xyP(x, ...
... •True if there is a y for which P(x,y) is true for every x. (i.e., true for a particular y regardless (or independent) of x) •False if for every y there is an x for which P(x,y) is false. Note that order matters here In particular, if yxP(x,y) is true, then xyP(x,y) is true. However, if xyP(x, ...
The Fundamental Theorem of World Theory
... ∅ as the value of every false sentence. Sentences w |= ϕ are then interpreted to be true just in case the semantic value of ‘w’ is a member of the semantic value of ϕ. So endorsing EP commits one only to an ontology with a single possible world, although of course the domain of worlds might grow sig ...
... ∅ as the value of every false sentence. Sentences w |= ϕ are then interpreted to be true just in case the semantic value of ‘w’ is a member of the semantic value of ϕ. So endorsing EP commits one only to an ontology with a single possible world, although of course the domain of worlds might grow sig ...
Incompleteness in a General Setting
... of a coding system representing the syntax of an object language (typically, that of arithmetic) within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs o ...
... of a coding system representing the syntax of an object language (typically, that of arithmetic) within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs o ...
An Abridged Report - Association for the Advancement of Artificial
... of sentences. Because of this, the derivation from only knowing (1) and (2) to knowing (3) must be carried out completely outside the logic, as in McDermott and Doyle’s logic or in Reiter’s (in their case with appropriate metalogical arguments about fixed points or extensions). In this paper, we pre ...
... of sentences. Because of this, the derivation from only knowing (1) and (2) to knowing (3) must be carried out completely outside the logic, as in McDermott and Doyle’s logic or in Reiter’s (in their case with appropriate metalogical arguments about fixed points or extensions). In this paper, we pre ...
Outline of Lecture 2 First Order Logic and Second Order Logic Basic
... • MSOL has no complete provability system: The Peano axioms are expressible in MSOL and characterize the structure h IN, +, ×, 0, 1i up to isomorphims. If there were a complete provability system, the set of MSOL(τarith )sentences true in h IN, +, ×, 0, 1i would be computable. But this contradicts G ...
... • MSOL has no complete provability system: The Peano axioms are expressible in MSOL and characterize the structure h IN, +, ×, 0, 1i up to isomorphims. If there were a complete provability system, the set of MSOL(τarith )sentences true in h IN, +, ×, 0, 1i would be computable. But this contradicts G ...
p and q
... •True if there is a y for which P(x,y) is true for every x. (i.e., true for a particular y regardless (or independent) of x) •False if for every y there is an x for which P(x,y) is false. Note that order matters here In particular, if yxP(x,y) is true, then xyP(x,y) is true. However, if xyP(x, ...
... •True if there is a y for which P(x,y) is true for every x. (i.e., true for a particular y regardless (or independent) of x) •False if for every y there is an x for which P(x,y) is false. Note that order matters here In particular, if yxP(x,y) is true, then xyP(x,y) is true. However, if xyP(x, ...
1. Sets, relations and functions. 1.1. Set theory. We assume the
... We say p is an ordered pair if there exist objects a and b such that p = (a, b). It follows from the preceding Proposition that if a and b are uniquely determined so we may define the first coordinate of p to be a and the second coordinate of (a, b) to be b. A relation is a set whose members are ord ...
... We say p is an ordered pair if there exist objects a and b such that p = (a, b). It follows from the preceding Proposition that if a and b are uniquely determined so we may define the first coordinate of p to be a and the second coordinate of (a, b) to be b. A relation is a set whose members are ord ...
Analysis of the paraconsistency in some logics
... satisfying, on this paper, Con1, Con2 and Con3 and a set of formulas. We will say that Γ is a theory of L if Γ ⊆ L. We will also say that Γ is closed if it contains all of its consequences (the converse of Con1.) For our purposes, F or is a numerable set of symbols from the language that contains ¬ ...
... satisfying, on this paper, Con1, Con2 and Con3 and a set of formulas. We will say that Γ is a theory of L if Γ ⊆ L. We will also say that Γ is closed if it contains all of its consequences (the converse of Con1.) For our purposes, F or is a numerable set of symbols from the language that contains ¬ ...
Frege, Boolos, and Logical Objects
... research on consistent Frege-style systems.2 In an important series of papers, George Boolos also developed systems for reconstructing Frege’s work. We’ll focus on the work in Boolos [1986], [1987], [1989], and [1993]. Although in [1986] and [1993] Boolos offers reconstructions of Basic Law V that ar ...
... research on consistent Frege-style systems.2 In an important series of papers, George Boolos also developed systems for reconstructing Frege’s work. We’ll focus on the work in Boolos [1986], [1987], [1989], and [1993]. Although in [1986] and [1993] Boolos offers reconstructions of Basic Law V that ar ...
Chapter 2, Logic
... of claim that can be either true of false. Some logicians prefer to talk of sentences, on the grounds that that gives us a definite subject for discussion. The supporters of ‘proposition’ retort that the meanings of words can change, words can be ambiguous, the same sentence can mean different thing ...
... of claim that can be either true of false. Some logicians prefer to talk of sentences, on the grounds that that gives us a definite subject for discussion. The supporters of ‘proposition’ retort that the meanings of words can change, words can be ambiguous, the same sentence can mean different thing ...
INTERMEDIATE LOGIC – Glossary of key terms
... A logical operator represented by a symbol in digital logic, with one or two inputs and a single output, which can be joined together in logic circuits. Logical operator Lesson 1, page 10 Words (representable by symbols) that combine or modify simple propositions, making them compound (such as AND, ...
... A logical operator represented by a symbol in digital logic, with one or two inputs and a single output, which can be joined together in logic circuits. Logical operator Lesson 1, page 10 Words (representable by symbols) that combine or modify simple propositions, making them compound (such as AND, ...
Chapter 11: Other Logical Tools Syllogisms and Quantification
... claim of the second premise that at least one M is an S. Once this is done, we see that the picture we have created is consistent with the conclusion that at least one M is not a B as shown by the fact that there is an X in the M circle but not in the B circle. Thus, 11-4 is valid. If the conclusion ...
... claim of the second premise that at least one M is an S. Once this is done, we see that the picture we have created is consistent with the conclusion that at least one M is not a B as shown by the fact that there is an X in the M circle but not in the B circle. Thus, 11-4 is valid. If the conclusion ...
Lecture 11 Artificial Intelligence Predicate Logic
... using symbols. – Symbols represent facts: P, Q, etc.. – These are joined by logical connectives (and, or, implication) e.g., P Q; Q R ...
... using symbols. – Symbols represent facts: P, Q, etc.. – These are joined by logical connectives (and, or, implication) e.g., P Q; Q R ...
Factoring out the impossibility of logical aggregation
... P. Mongin / Journal of Economic Theory 141 (2008) 100 – 113 ...
... P. Mongin / Journal of Economic Theory 141 (2008) 100 – 113 ...
Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus (Latin for ""Logico-Philosophical Treatise"") is the only book-length philosophical work published by the German-Austrian philosopher Ludwig Wittgenstein in his lifetime. The project had a broad aim – to identify the relationship between language and reality and to define the limits of science – and is recognized as a significant philosophical work of the twentieth century. G. E. Moore originally suggested the work's Latin title as homage to the Tractatus Theologico-Politicus by Baruch Spinoza.Wittgenstein wrote the notes for the Tractatus while he was a soldier during World War I and completed it when a prisoner of war at Como and later Cassino in August 1918. It was first published in German in 1921 as Logisch-Philosophische Abhandlung. The Tractatus was influential chiefly amongst the logical positivists of the Vienna Circle, such as Rudolf Carnap and Friedrich Waismann. Bertrand Russell's article ""The Philosophy of Logical Atomism"" is presented as a working out of ideas that he had learned from Wittgenstein.The Tractatus employs a notoriously austere and succinct literary style. The work contains almost no arguments as such, but rather consists of declarative statements that are meant to be self-evident. The statements are hierarchically numbered, with seven basic propositions at the primary level (numbered 1–7), with each sub-level being a comment on or elaboration of the statement at the next higher level (e.g., 1, 1.1, 1.11, 1.12).Wittgenstein's later works, notably the posthumously published Philosophical Investigations, criticised many of the ideas in the Tractatus.