Propositional Logic .
... Q1: how many different binary symbols can we define ? Q2: what is the minimal number of such symbols? ...
... Q1: how many different binary symbols can we define ? Q2: what is the minimal number of such symbols? ...
Clausal Logic and Logic Programming in Algebraic Domains*
... In this paper we show how to represent the Smyth powerdomain of a coherent algebraic dcpo using an elementary logic built over such a domain. This is a clausal logic, different from the modal logic introduced by Winskel [Win83] for the Smyth powerdomain. We obtain the logic by regarding finite sets ...
... In this paper we show how to represent the Smyth powerdomain of a coherent algebraic dcpo using an elementary logic built over such a domain. This is a clausal logic, different from the modal logic introduced by Winskel [Win83] for the Smyth powerdomain. We obtain the logic by regarding finite sets ...
Sets
... Standard Symbols which denote sets of numbers N : The set of all natural numbers (i.e.,all positive integers) Z : The set of all integers Z+ : The set of all positive integers Z* : The set of all nonzero integers E : The set of all even integers Q : The set of all rational numbers Q* ...
... Standard Symbols which denote sets of numbers N : The set of all natural numbers (i.e.,all positive integers) Z : The set of all integers Z+ : The set of all positive integers Z* : The set of all nonzero integers E : The set of all even integers Q : The set of all rational numbers Q* ...
WhichQuantifiersLogical
... and quantifiers is to be established semantically in one way or another prior to their inferential role. Their meanings may be the primitives of our reasoning in general“and”, “or”, “not”, “if…then”, “all”, “some”or they may be understood informally like “most”, “has the same number as”, etc. in a ...
... and quantifiers is to be established semantically in one way or another prior to their inferential role. Their meanings may be the primitives of our reasoning in general“and”, “or”, “not”, “if…then”, “all”, “some”or they may be understood informally like “most”, “has the same number as”, etc. in a ...
Decision Procedures for Flat Array Properties
... like Presburger arithmetic. We also provide suitable decision procedures for Flat Array Properties of both settings. Such procedures reduce the decidability of Flat Array Properties to the decidability of T -formulæ in one case and TI - and TE -formulæ in the other case. We further show, as an appli ...
... like Presburger arithmetic. We also provide suitable decision procedures for Flat Array Properties of both settings. Such procedures reduce the decidability of Flat Array Properties to the decidability of T -formulæ in one case and TI - and TE -formulæ in the other case. We further show, as an appli ...
Properties of Independently Axiomatizable Bimodal Logics
... obtained are called transfer theorems in Fine and Schurz [91] and are of the following type. Let L 63 ⊥ be an independently axiomatizable bimodal logic and L2 as well as L its mono-modal fragments. Then L has a property P iff L2 and L have P . Properties which will be discussed are completeness, f ...
... obtained are called transfer theorems in Fine and Schurz [91] and are of the following type. Let L 63 ⊥ be an independently axiomatizable bimodal logic and L2 as well as L its mono-modal fragments. Then L has a property P iff L2 and L have P . Properties which will be discussed are completeness, f ...
ON A MINIMAL SYSTEM OF ARISTOTLE`S SYLLOGISTIC Introduction
... The inductive definition of the notion of truth in the model MS for an arbitrary formula α is the same as for ML . Let S be the set of all models MS (models based on I S with different sets B and functions f and g). We shall understand that a formula is valid in S iff it is true in all models from S ...
... The inductive definition of the notion of truth in the model MS for an arbitrary formula α is the same as for ML . Let S be the set of all models MS (models based on I S with different sets B and functions f and g). We shall understand that a formula is valid in S iff it is true in all models from S ...
G - Courses
... obtained from Herbrand structures via taking the equivalence classes of terms according to the equalities between them in some structure satisfying the FO-sentence at hand. Here, we used the resolution procedure only for formulas of propositional logic. The resolution procedure can be extended to ...
... obtained from Herbrand structures via taking the equivalence classes of terms according to the equalities between them in some structure satisfying the FO-sentence at hand. Here, we used the resolution procedure only for formulas of propositional logic. The resolution procedure can be extended to ...
deductive system
... not in L. In a Gentzen system, all axioms are of the form A ⇒ A, for each formula A in L. Theorems in a Gentzen system are those formulas B (in L) such that ⇒ B is the conclusion of a deduction. • tableau system: in a tableau system, like natural deduction, there are only inference rules and no axio ...
... not in L. In a Gentzen system, all axioms are of the form A ⇒ A, for each formula A in L. Theorems in a Gentzen system are those formulas B (in L) such that ⇒ B is the conclusion of a deduction. • tableau system: in a tableau system, like natural deduction, there are only inference rules and no axio ...
Deciding Global Partial-Order Properties
... be exploited to reduce the state-space explosion problem: the cost of generating at least one representative per equivalence class is typically significantly less than the cost of generating all interleavings [5,9, 10, 151. If the specification could distinguish between two sequences of the same equ ...
... be exploited to reduce the state-space explosion problem: the cost of generating at least one representative per equivalence class is typically significantly less than the cost of generating all interleavings [5,9, 10, 151. If the specification could distinguish between two sequences of the same equ ...
Resources - CSE, IIT Bombay
... interpretations over all domains in order to prove unsatisfiability Instead, we try to fix a special domain (called a Herbrand universe) such that the formula, S, is unsatisfiable iff it is false under all the interpretations over this domain ...
... interpretations over all domains in order to prove unsatisfiability Instead, we try to fix a special domain (called a Herbrand universe) such that the formula, S, is unsatisfiable iff it is false under all the interpretations over this domain ...
Implicative Formulae in the Vroofs as Computations” Analogy
... Fixed a theory T, there exists an obvious monoidal category C(T) freely generatedby T. For many respects,it is easier to work in this free category, than in the original logic framework. The most important advantage is that it is simpler to handle arrows of the category than derivationsof the logic. ...
... Fixed a theory T, there exists an obvious monoidal category C(T) freely generatedby T. For many respects,it is easier to work in this free category, than in the original logic framework. The most important advantage is that it is simpler to handle arrows of the category than derivationsof the logic. ...
Predicate logic
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
Logic - Mathematical Institute SANU
... incorrect ones involves considering both. With more reason, it is often put into the definition of logic that it is concerned with formal deduction. This means that logic is concerned with laws of correct deduction based uniquely on the meaning of some particular words called logical constants. In d ...
... incorrect ones involves considering both. With more reason, it is often put into the definition of logic that it is concerned with formal deduction. This means that logic is concerned with laws of correct deduction based uniquely on the meaning of some particular words called logical constants. In d ...
A Propositional Modal Logic for the Liar Paradox Martin Dowd
... and can be considered to be a set of integers, as Kurt Godel essentially pointed out in 1933. Since among the statements of mathematics are statements about the integers, one can in this way devise statements which refer to themselves. One is immediately prompted to ask whether “this statement is fa ...
... and can be considered to be a set of integers, as Kurt Godel essentially pointed out in 1933. Since among the statements of mathematics are statements about the integers, one can in this way devise statements which refer to themselves. One is immediately prompted to ask whether “this statement is fa ...
full text (.pdf)
... We consider two related decision problems: given a rule of the form (1), (i) is it relationally valid? That is, is it true in all relational models? (ii) is it derivable in PHL? The paper Kozen 2000] considered problem (i) only. We show that both of these problems are PSPACE -hard by a single reduc ...
... We consider two related decision problems: given a rule of the form (1), (i) is it relationally valid? That is, is it true in all relational models? (ii) is it derivable in PHL? The paper Kozen 2000] considered problem (i) only. We show that both of these problems are PSPACE -hard by a single reduc ...
Mathematical Logic Deciding logical consequence Complexity of
... But... Formal proofs are bloated and over expanded! I find nothing in [formal logic] but shackles. It does not help us at all in the direction of conciseness, far from it; and if it requires 27 equations to establish that 1 is a number, how many will it require to demonstrate a real theorem? (Poinca ...
... But... Formal proofs are bloated and over expanded! I find nothing in [formal logic] but shackles. It does not help us at all in the direction of conciseness, far from it; and if it requires 27 equations to establish that 1 is a number, how many will it require to demonstrate a real theorem? (Poinca ...
Logic - Decision Procedures
... Q1: how many different binary symbols can we define ? Q2: what is the minimal number of such symbols? ...
... Q1: how many different binary symbols can we define ? Q2: what is the minimal number of such symbols? ...
Predicate logic - Teaching-WIKI
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
Predicate logic
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
First-order logic;
... Representation: Understand the relationships between different representations of the same information or idea. I ...
... Representation: Understand the relationships between different representations of the same information or idea. I ...
Predicate Calculus - National Taiwan University
... Our only alternative is proof procedures! Therefore the soundness and completeness of our proof procedures is very important! ...
... Our only alternative is proof procedures! Therefore the soundness and completeness of our proof procedures is very important! ...
Set Theory II
... Powers For each set there exists a collection of sets that contains among its elements all the subsets of the given set. (Combined with the Axiom of Specification, it follows that if A is a set, then P(A) = {B : B ⊆ A} is also a set.) Regularity Every non-empty set contains an element that is disjoi ...
... Powers For each set there exists a collection of sets that contains among its elements all the subsets of the given set. (Combined with the Axiom of Specification, it follows that if A is a set, then P(A) = {B : B ⊆ A} is also a set.) Regularity Every non-empty set contains an element that is disjoi ...
03_Artificial_Intelligence-PredicateLogic
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
Predicate Logic
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...