full text (.pdf)
... deterministic PDL, but neither the upper nor the lower bound of our PSPACE completeness result follows from theirs. Not only are PDL semantics restricted to relational models, but the arguments of Halpern and Reif 1983] depend on an additional nonalgebraic restriction: the relations interpreting at ...
... deterministic PDL, but neither the upper nor the lower bound of our PSPACE completeness result follows from theirs. Not only are PDL semantics restricted to relational models, but the arguments of Halpern and Reif 1983] depend on an additional nonalgebraic restriction: the relations interpreting at ...
chapter1p3 - WordPress.com
... All but the final proposition are called premises. The last statement is the conclusion. The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no matter what propositions are substituted into its propositional variables. If the premises are p1 ...
... All but the final proposition are called premises. The last statement is the conclusion. The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no matter what propositions are substituted into its propositional variables. If the premises are p1 ...
(pdf)
... given a set of atomic or prime formulae, which intuitively can be thought of as possessing truth values (true or false). Here the prime formulae will be propositional variables, as well as a constant > for truth. It is also common to include a constant for falsity, and possibly non-logical constants ...
... given a set of atomic or prime formulae, which intuitively can be thought of as possessing truth values (true or false). Here the prime formulae will be propositional variables, as well as a constant > for truth. It is also common to include a constant for falsity, and possibly non-logical constants ...
EVERYONE KNOWS THAT SOMEONE KNOWS
... (w, ρ[x 7→ α(c)]) 2A ψ is equivalent to (u, ρ[x 7→ α(c)]) ψ being true for all u ∈ W such that w ∼α(A∩C)∪ρ[x7→α(c)](A∩V ) u. By the induction hypothesis, the last statement is equivalent to (u, ρ) ψ[c/x] being true for all u ∈ W such that w ∼α(A∩C)∪ρ[x7→α(c)](A∩V ) u. By Definition 2, it is al ...
... (w, ρ[x 7→ α(c)]) 2A ψ is equivalent to (u, ρ[x 7→ α(c)]) ψ being true for all u ∈ W such that w ∼α(A∩C)∪ρ[x7→α(c)](A∩V ) u. By the induction hypothesis, the last statement is equivalent to (u, ρ) ψ[c/x] being true for all u ∈ W such that w ∼α(A∩C)∪ρ[x7→α(c)](A∩V ) u. By Definition 2, it is al ...
First Order Predicate Logic
... (∀x) ((MAN(x) → MORTAL(x)) Λ MAN(john)) → MORTAL(john) Prof Saroj Kaushik, CSE, IIT Delhi ...
... (∀x) ((MAN(x) → MORTAL(x)) Λ MAN(john)) → MORTAL(john) Prof Saroj Kaushik, CSE, IIT Delhi ...
Refining Internet and Database Searches
... • Using quotation marks when searching instructs the search engine to return only websites and documents with those exact words. • Quotation marks work best with phrases. • For example, google Shakespeare’s wife and 675,000 results appear. • However, put the phrase in quotation marks “Shakespeare’s ...
... • Using quotation marks when searching instructs the search engine to return only websites and documents with those exact words. • Quotation marks work best with phrases. • For example, google Shakespeare’s wife and 675,000 results appear. • However, put the phrase in quotation marks “Shakespeare’s ...
MMConceptualComputationalRemainder
... the maximum of the set of common divisors of the two numbers, and a set of numbers has only one maximum. I have shown my students this proof many times, but they almost never reproduce it on an examination. ...
... the maximum of the set of common divisors of the two numbers, and a set of numbers has only one maximum. I have shown my students this proof many times, but they almost never reproduce it on an examination. ...
tasks 41
... clause form (CNF-form) Add the negation of what is to be proved, in clause form, to the set axioms Resolve these clauses together, producing new clauses that logically follow from them Produce a contradiction by generating the empty clause ...
... clause form (CNF-form) Add the negation of what is to be proved, in clause form, to the set axioms Resolve these clauses together, producing new clauses that logically follow from them Produce a contradiction by generating the empty clause ...
Everything is Knowable - Computer Science Intranet
... cannot be believed after being announced. Both are quite different from Moore’s original analysis that p ∧ ¬Kp cannot be sincerely announced/uttered! Unlike the single-agent version, the multi-agent version of the Moore-sentence is not problematic. If I tell you “You don’t know that I play the cello ...
... cannot be believed after being announced. Both are quite different from Moore’s original analysis that p ∧ ¬Kp cannot be sincerely announced/uttered! Unlike the single-agent version, the multi-agent version of the Moore-sentence is not problematic. If I tell you “You don’t know that I play the cello ...
Logic Programming, Functional Programming, and Inductive
... Essentially, they develop the theory of inductive definitions so as to distinguish divergent computations from finite failures. Negation goes beyond monotone inductive definitions: with negated subgoals, the function φ above may not be monotone. However, perhaps the database can be partitioned into ...
... Essentially, they develop the theory of inductive definitions so as to distinguish divergent computations from finite failures. Negation goes beyond monotone inductive definitions: with negated subgoals, the function φ above may not be monotone. However, perhaps the database can be partitioned into ...
Document
... If P(x) is the statement “x has won a race” where the domain of discourse is all runners, then the universal quantification of P(x) is x P ( x ) , i.e., every runner has won a race. The negation of this statement is “it is not the case that every runner has won a race. Therefore there exists at l ...
... If P(x) is the statement “x has won a race” where the domain of discourse is all runners, then the universal quantification of P(x) is x P ( x ) , i.e., every runner has won a race. The negation of this statement is “it is not the case that every runner has won a race. Therefore there exists at l ...
34-2.pdf
... devoted to a perhaps not entirely central result (although this choice is partly a matter of personal taste). For some of the more specialized proofs, a condensed version could be given. (On the positive side, the author does often have some informal discussion of the goal behind a proof.) — A summa ...
... devoted to a perhaps not entirely central result (although this choice is partly a matter of personal taste). For some of the more specialized proofs, a condensed version could be given. (On the positive side, the author does often have some informal discussion of the goal behind a proof.) — A summa ...
Document
... arbitrary selection rule (due to trapping in infinite derivations). Note 2: The theorem applies to safe interpreters that adopt selection rules that are safe (do not select negative literals that are not ground), unlike most Prolog interpreters. 30 October 2005 ...
... arbitrary selection rule (due to trapping in infinite derivations). Note 2: The theorem applies to safe interpreters that adopt selection rules that are safe (do not select negative literals that are not ground), unlike most Prolog interpreters. 30 October 2005 ...
Geometric Modal Logic
... claims incomparably more than saying that this proposition is simply necessary. Speaking of something as ‘possibly possible’, we implicitly let the variation system itself vary, we shift from a given system of possibility into a frame inside which this system is only one among others, and we say tha ...
... claims incomparably more than saying that this proposition is simply necessary. Speaking of something as ‘possibly possible’, we implicitly let the variation system itself vary, we shift from a given system of possibility into a frame inside which this system is only one among others, and we say tha ...
Logic Handout - EECS: www
... expression that we will write is called the “sum-of-products” canonical form. This canonical form gets its name from the fact that it is formed by taking the sum (OR) of a set of terms, each term being a product (AND) of input variables or their complements. Every place (row) where a 1 appears in th ...
... expression that we will write is called the “sum-of-products” canonical form. This canonical form gets its name from the fact that it is formed by taking the sum (OR) of a set of terms, each term being a product (AND) of input variables or their complements. Every place (row) where a 1 appears in th ...
Conjunctive normal form - Computer Science and Engineering
... However, the following formulas are NOT in DNF: — NOT is the outermost operator — an OR is nested within an AND Converting a formula to DNF involves using logical equivalences, such as the double negative elimination, De Morgan's laws, and the distributive law. All logical formulas can be converted ...
... However, the following formulas are NOT in DNF: — NOT is the outermost operator — an OR is nested within an AND Converting a formula to DNF involves using logical equivalences, such as the double negative elimination, De Morgan's laws, and the distributive law. All logical formulas can be converted ...
Modalities in the Realm of Questions: Axiomatizing Inquisitive
... categories are intertwined: from a sequence of declaratives, clause (iii) allows us to form a basic interrogative, from which more complex interrogatives may be formed by means of clauses (iv) and (v). On the other hand, clauses (vi) and (vii) allow us to embed an interrogative under a modality, res ...
... categories are intertwined: from a sequence of declaratives, clause (iii) allows us to form a basic interrogative, from which more complex interrogatives may be formed by means of clauses (iv) and (v). On the other hand, clauses (vi) and (vii) allow us to embed an interrogative under a modality, res ...
Boolean unification with predicates
... We will henceforth refer to the 2nd problem in this list as Boolean unification (BU). In this article, we extend the research on BU by analysing the following more general problem: Problem (Boolean unification with predicates (BUP)) For an input formula F[X ] in first-order logic with equality conta ...
... We will henceforth refer to the 2nd problem in this list as Boolean unification (BU). In this article, we extend the research on BU by analysing the following more general problem: Problem (Boolean unification with predicates (BUP)) For an input formula F[X ] in first-order logic with equality conta ...
Logics of Truth - Project Euclid
... truth are then the standard Tarski ones, where propositions are the objects of the truth predicate. In an important sense these axioms reflect the minimal conditions one would expect of any theory of truth. The other theories we shall consider all have the above theory as a consequence. 3.1 Models o ...
... truth are then the standard Tarski ones, where propositions are the objects of the truth predicate. In an important sense these axioms reflect the minimal conditions one would expect of any theory of truth. The other theories we shall consider all have the above theory as a consequence. 3.1 Models o ...
CHAPTER 1 The main subject of Mathematical Logic is
... stick to the use of bound variables. In the definition of “substitution of expression E 0 for variable x in expression E”, either one requires that no variable free in E 0 becomes bound by a variable-binding operator in E, when the free occurrences of x are replaced by E 0 (also expressed by saying ...
... stick to the use of bound variables. In the definition of “substitution of expression E 0 for variable x in expression E”, either one requires that no variable free in E 0 becomes bound by a variable-binding operator in E, when the free occurrences of x are replaced by E 0 (also expressed by saying ...