A HIGHER-ORDER FINE-GRAINED LOGIC FOR INTENSIONAL
... It has frequently been noted that the characterization of intensions as functions from indices to denotations, as in Montague (1974), yields a semantics which is not sufficiently finegrained. For example, logically equivalent expressions are co-intensional and so intersubstitutable in all contexts, ...
... It has frequently been noted that the characterization of intensions as functions from indices to denotations, as in Montague (1974), yields a semantics which is not sufficiently finegrained. For example, logically equivalent expressions are co-intensional and so intersubstitutable in all contexts, ...
Between Truth and Falsity
... it is impossible for A to be false or indeterminate. Hence it is valid. (But in fact there are no valid formulas in K3) Test for unexceptionability Assume B. If this leads to a contradiction, then the formula must be always either true or indeterminate. Test for contradictoriness Assume formula is ...
... it is impossible for A to be false or indeterminate. Hence it is valid. (But in fact there are no valid formulas in K3) Test for unexceptionability Assume B. If this leads to a contradiction, then the formula must be always either true or indeterminate. Test for contradictoriness Assume formula is ...
Lectures on Laws of Supply and Demand, Simple and Compound
... Definition A compound proposition is two or more propositions combined by a logical connective. Example 2 “ If Brian and Angela are not both happy then either Brian is not happy or Angela is not happy”. This is an example of a compound proposition. Logic is not concerned with determining the truth ...
... Definition A compound proposition is two or more propositions combined by a logical connective. Example 2 “ If Brian and Angela are not both happy then either Brian is not happy or Angela is not happy”. This is an example of a compound proposition. Logic is not concerned with determining the truth ...
On the Interpretation of Intuitionistic Logic
... “a is false” does not satisfy the above principle. To avoid such circumstances, Brouwer gives a new definition of negation: “a is false” should mean “a leads to a contradiction”. Thus the negation of a is transformed in to an existential statement: “There exists a chain of logical deductions which l ...
... “a is false” does not satisfy the above principle. To avoid such circumstances, Brouwer gives a new definition of negation: “a is false” should mean “a leads to a contradiction”. Thus the negation of a is transformed in to an existential statement: “There exists a chain of logical deductions which l ...
1. Binary operators and their representations
... Duality principle states that every algebraic expression is deducible if the operators and the identity elements are interchanged. Identity elements: ...
... Duality principle states that every algebraic expression is deducible if the operators and the identity elements are interchanged. Identity elements: ...
January 12
... Such limitations of Aristotelian logic give Frege criteria for the adequacy of a proper logical notation, or Begriffsschrift. Such a notation must be able to do 2 things: A. express all (and only) propositions, i.e., all and only things that are either true or false; and B. state all logical relati ...
... Such limitations of Aristotelian logic give Frege criteria for the adequacy of a proper logical notation, or Begriffsschrift. Such a notation must be able to do 2 things: A. express all (and only) propositions, i.e., all and only things that are either true or false; and B. state all logical relati ...
Sample pages 1 PDF
... Mathematics and some other disciplines such as computer science often consider domains of individuals in which certain relations and operations are singled out. When using the language of propositional logic, our ability to talk about the properties of such relations and operations is very limited. ...
... Mathematics and some other disciplines such as computer science often consider domains of individuals in which certain relations and operations are singled out. When using the language of propositional logic, our ability to talk about the properties of such relations and operations is very limited. ...
on Computability
... stop when it is run for some input. Computing system S(p,i), which computes a function with a pair of inputs that are a program p, and an input i for that program of p, then, we are writing a program P which will take a pair (Sj(q,i), j) as an input, and gives an answer of ...
... stop when it is run for some input. Computing system S(p,i), which computes a function with a pair of inputs that are a program p, and an input i for that program of p, then, we are writing a program P which will take a pair (Sj(q,i), j) as an input, and gives an answer of ...
Answer Sets for Propositional Theories
... (i) Γ1 is strongly equivalent to Γ2 , (ii) Γ1 is equivalent to Γ2 in the logic of here-and-there, and (iii) for each set X of atoms, Γ1X is equivalent to Γ2X in classical logic. The equivalence between (i) and (ii) is a generalization of the main result of [Lifschitz et al., 2001], and it is an imme ...
... (i) Γ1 is strongly equivalent to Γ2 , (ii) Γ1 is equivalent to Γ2 in the logic of here-and-there, and (iii) for each set X of atoms, Γ1X is equivalent to Γ2X in classical logic. The equivalence between (i) and (ii) is a generalization of the main result of [Lifschitz et al., 2001], and it is an imme ...
7 LOGICAL AGENTS
... • Sentence follows logically from sentence , , if and only if (iff) in every model in which is true, is also true • In other words: if is true, then must also be true • We say that the sentence entails the sentence • Consider the squares [1,2], [2,2], and [3,1] in the wumpus-world and the question w ...
... • Sentence follows logically from sentence , , if and only if (iff) in every model in which is true, is also true • In other words: if is true, then must also be true • We say that the sentence entails the sentence • Consider the squares [1,2], [2,2], and [3,1] in the wumpus-world and the question w ...
Incompleteness - the UNC Department of Computer Science
... theory. In 1977, Kirby, Paris and Harrington proved that a statement in combinatorics, a version of the Ramsey theorem, is undecidable in the axiomatization of arithmetic given by the Peano axioms but can be proven to be true in the larger system of set theory. Kruskal's tree theorem, which has appl ...
... theory. In 1977, Kirby, Paris and Harrington proved that a statement in combinatorics, a version of the Ramsey theorem, is undecidable in the axiomatization of arithmetic given by the Peano axioms but can be proven to be true in the larger system of set theory. Kruskal's tree theorem, which has appl ...
pdf file
... 2. Introduce general theorems for manipulating quantified expressions and prove these theorems formally. 3. Introduce metatheorems for removal and introduction of quantification, prove them, and show some simple examples of how the metatheorems are used. ...
... 2. Introduce general theorems for manipulating quantified expressions and prove these theorems formally. 3. Introduce metatheorems for removal and introduction of quantification, prove them, and show some simple examples of how the metatheorems are used. ...
Kripke Semantics for Basic Sequent Systems
... 2. Limiting the allowed set of context-formulas (as in (2), where only 2-formulas may appear on the left, and no context-formulas are allowed on the right). 3. Modifying some context-formulas in the rule application (as in (3), where Γ1 in the premise becomes 2Γ1 in the conclusion). To deal with the ...
... 2. Limiting the allowed set of context-formulas (as in (2), where only 2-formulas may appear on the left, and no context-formulas are allowed on the right). 3. Modifying some context-formulas in the rule application (as in (3), where Γ1 in the premise becomes 2Γ1 in the conclusion). To deal with the ...