Notes on the ACL2 Logic
... But what we are after is reasoning about programs, and while propositional logic will play an important role, we need more powerful logics. To see why, let’s simplify things for a moment and consider conjectures involving numbers and arithmetic operations. Consider the conjecture: 1. a+b = ba What d ...
... But what we are after is reasoning about programs, and while propositional logic will play an important role, we need more powerful logics. To see why, let’s simplify things for a moment and consider conjectures involving numbers and arithmetic operations. Consider the conjecture: 1. a+b = ba What d ...
The Computer Modelling of Mathematical Reasoning Alan Bundy
... This book started as notes for a postgraduate course in Mathematical Reasoning given in the Department of Artificial Intelligence at Edinburgh from 1979 onwards. Students on the course are drawn from a wide range of backgrounds: Psychology, Computer Science, Mathematics, Education, etc. The first dr ...
... This book started as notes for a postgraduate course in Mathematical Reasoning given in the Department of Artificial Intelligence at Edinburgh from 1979 onwards. Students on the course are drawn from a wide range of backgrounds: Psychology, Computer Science, Mathematics, Education, etc. The first dr ...
Arithmetics in finite but potentially infinite worlds ∀ ∃ ∀ ∃
... statistical representability and weak statistical representability. We show that the relations which can be represented by these methods are the Σ2 , ∆2 and Π3 relations, respectively. Thus, the second of these methods is no more powerful than the original FM–representability concept introduced by M ...
... statistical representability and weak statistical representability. We show that the relations which can be represented by these methods are the Σ2 , ∆2 and Π3 relations, respectively. Thus, the second of these methods is no more powerful than the original FM–representability concept introduced by M ...
Euclidian Roles in Description Logics
... For example, in [2] the Description Logic RIQ is extended with several role axioms, like reflexive and irreflexive role axioms, disjoint role axioms and simple negation on roles. These extensions has motivated us to investigate possibilities of extending Description Logics with other role axioms. In ...
... For example, in [2] the Description Logic RIQ is extended with several role axioms, like reflexive and irreflexive role axioms, disjoint role axioms and simple negation on roles. These extensions has motivated us to investigate possibilities of extending Description Logics with other role axioms. In ...
First-Order Theorem Proving and VAMPIRE
... put formulas, for example ennf transformation and cnf transformation. Preprocessing is discussion in Section 5. The input formulas are finally converted to clauses, after which VAMPIRE tries to check unsatisfiability of the resulting set of clauses using the resolution and superposition inference sy ...
... put formulas, for example ennf transformation and cnf transformation. Preprocessing is discussion in Section 5. The input formulas are finally converted to clauses, after which VAMPIRE tries to check unsatisfiability of the resulting set of clauses using the resolution and superposition inference sy ...
Carnap and Quine on the analytic-synthetic - Philsci
... list of pairs of opposite concepts that have been used by Quine and Carnap, such as analytic/synthetic, logical/factual, logical/descriptive, a priori/a posteriori, internal/external, necessary/contingent, which in one way or another have all been equated to the general analytic/synthetic distinctio ...
... list of pairs of opposite concepts that have been used by Quine and Carnap, such as analytic/synthetic, logical/factual, logical/descriptive, a priori/a posteriori, internal/external, necessary/contingent, which in one way or another have all been equated to the general analytic/synthetic distinctio ...
A Logic for Perception and Belief Department of Computer Science
... new beliefs is sensory input. The connection between perception and logic is difficult and multifacetted. Ma&worth and Reiter [12], for example, explore the connection between vision and default reasoning. We do not address that, nor many other diEcult issues in relating perception and logic. Instea ...
... new beliefs is sensory input. The connection between perception and logic is difficult and multifacetted. Ma&worth and Reiter [12], for example, explore the connection between vision and default reasoning. We do not address that, nor many other diEcult issues in relating perception and logic. Instea ...
Peano`s Arithmetic
... of logical reform for the philosophy of mathematics. It was through hearing discussions between Peano of Turin and the other assembled philosophers that I became aware of this… I was impressed by the fact that…he showed more precision and more logical rigor than anybody else. I went to him and said ...
... of logical reform for the philosophy of mathematics. It was through hearing discussions between Peano of Turin and the other assembled philosophers that I became aware of this… I was impressed by the fact that…he showed more precision and more logical rigor than anybody else. I went to him and said ...
Implicit Hitting Set Algorithms for Reasoning Beyond NP
... predicate check (Line 4) and, if this check fails to verify that a candidate is an actual solution, core extraction (Line 5). The basic idea of the algorithm is to guide the search by maintaining a set of computed cores K of the given problem and iteratively generating minimum-cost hitting sets of K ...
... predicate check (Line 4) and, if this check fails to verify that a candidate is an actual solution, core extraction (Line 5). The basic idea of the algorithm is to guide the search by maintaining a set of computed cores K of the given problem and iteratively generating minimum-cost hitting sets of K ...
ATL with Strategy Contexts and Bounded Memory
... Our contributions. In this paper, we extend ATL and ATL in two directions: first, while ATL strategy quantifiers drop strategies introduced by earlier quantifiers in the evaluation of the formula, our logics keep executing those strategies. To achieve this idea, we naturally adapt the semantics of ATL ...
... Our contributions. In this paper, we extend ATL and ATL in two directions: first, while ATL strategy quantifiers drop strategies introduced by earlier quantifiers in the evaluation of the formula, our logics keep executing those strategies. To achieve this idea, we naturally adapt the semantics of ATL ...
Yablo`s paradox
... involved, and a fortiori no fixed-point predicate. We therefore have a paradox without circularity.6 Such a suggestion would be disingenuous, though. As a matter of fact, we did not apply the ω-rule, and could not have. The reason we know that ¬Tsn is provable for all n is that we have a uniform pro ...
... involved, and a fortiori no fixed-point predicate. We therefore have a paradox without circularity.6 Such a suggestion would be disingenuous, though. As a matter of fact, we did not apply the ω-rule, and could not have. The reason we know that ¬Tsn is provable for all n is that we have a uniform pro ...
Foundations of Computation - Department of Mathematics and
... conclusion that “I am mortal” can be deduced by logic. Logical deduction is a kind of computation. By applying rules of logic to a given set of premises, conclusions that follow from those premises can be generated automatically, by a computational process which could be carried out by a computer. O ...
... conclusion that “I am mortal” can be deduced by logic. Logical deduction is a kind of computation. By applying rules of logic to a given set of premises, conclusions that follow from those premises can be generated automatically, by a computational process which could be carried out by a computer. O ...
AGM Postulates in Arbitrary Logics: Initial Results and - FORTH-ICS
... Since operators are not taken into account in our setting, the only way to “connect” expressions of the logic is by grouping them into sets of expressions. This type of “connective” will be heavily used, as in most cases we will develop results that deal with sets of expressions, instead of single e ...
... Since operators are not taken into account in our setting, the only way to “connect” expressions of the logic is by grouping them into sets of expressions. This type of “connective” will be heavily used, as in most cases we will develop results that deal with sets of expressions, instead of single e ...
x - Loughborough University Intranet
... Objects and properties versus statements (4) • Our interpretation is that those students who do not want to declare that the statement is false as soon as a counterexample is found are not considering the closed statement. They are working with the open statement “n2-n+11 is a prime number”, in whic ...
... Objects and properties versus statements (4) • Our interpretation is that those students who do not want to declare that the statement is false as soon as a counterexample is found are not considering the closed statement. They are working with the open statement “n2-n+11 is a prime number”, in whic ...
Proofs in Higher-Order Logic - ScholarlyCommons
... Expansion trees are defined rrs generalizations of Herbrand hqtauces for formulas in a nonextensional form of higher-order logic based on Church's simple theory of types. Such expansion trees can be defined with or without the use of skolem functions. These trees store substitution terms and either ...
... Expansion trees are defined rrs generalizations of Herbrand hqtauces for formulas in a nonextensional form of higher-order logic based on Church's simple theory of types. Such expansion trees can be defined with or without the use of skolem functions. These trees store substitution terms and either ...
THE LOGIC OF QUANTIFIED STATEMENTS
... • add quantifiers, words that refer to quantities such as “some” or “all” and tell for how many elements a given predicate is true. • e.g., For some integer x, x is divisible by 5 • e.g., For all integer x, x is divisible by 5 • e.g., there exists two integer x, such that x is divisible by 5. • All ...
... • add quantifiers, words that refer to quantities such as “some” or “all” and tell for how many elements a given predicate is true. • e.g., For some integer x, x is divisible by 5 • e.g., For all integer x, x is divisible by 5 • e.g., there exists two integer x, such that x is divisible by 5. • All ...