logic, programming and prolog (2ed)
... predicate logic including notions like language, interpretation, model, logical consequence, logical inference, soundness and completeness. The final section introduces the concept of substitution which is needed in subsequent chapters. Chapter 2 introduces the restricted language of definite progra ...
... predicate logic including notions like language, interpretation, model, logical consequence, logical inference, soundness and completeness. The final section introduces the concept of substitution which is needed in subsequent chapters. Chapter 2 introduces the restricted language of definite progra ...
DISCRETE MATHEMATICAL STRUCTURES
... Conditional Propositions: A proposition of the form ―if p then q‖ or ―p implies q‖, represented ―p → q‖ is called a conditional proposition. For instance: ―if John is from Chicago then John is from Illinois‖. The proposition p is called hypothesis or antecedent, and the proposition q is the conclusi ...
... Conditional Propositions: A proposition of the form ―if p then q‖ or ―p implies q‖, represented ―p → q‖ is called a conditional proposition. For instance: ―if John is from Chicago then John is from Illinois‖. The proposition p is called hypothesis or antecedent, and the proposition q is the conclusi ...
Abella: A System for Reasoning about Relational Specifications
... Computation and reasoning on linguistic structures goes back at least to Gödel and Church. For them, syntax was encoded as a string of symbols: we usually refer to that approach to syntax as concrete syntax. While concrete syntax has the advantage of being readable and writable by humans, it has ma ...
... Computation and reasoning on linguistic structures goes back at least to Gödel and Church. For them, syntax was encoded as a string of symbols: we usually refer to that approach to syntax as concrete syntax. While concrete syntax has the advantage of being readable and writable by humans, it has ma ...
The Foundations
... =>Example: Since it is not raining now(the current situation), the statement It_is_raining is false (in the current situation). But if it were raining now, then I would say that It_is_raining is true. Factors affecting the truth value of a proposition: the situation in which the proposition is u ...
... =>Example: Since it is not raining now(the current situation), the statement It_is_raining is false (in the current situation). But if it were raining now, then I would say that It_is_raining is true. Factors affecting the truth value of a proposition: the situation in which the proposition is u ...
Interpretability formalized
... shall use interpretations to compare theories. Furthermore, we shall also study interpretations as meta-mathematical entities. Roughly, an interpretation j of a theory T into a theory S (we write j : S¤T ) is a structure-preserving map, mapping axioms of T to theorems of S. Structurepreserving means ...
... shall use interpretations to compare theories. Furthermore, we shall also study interpretations as meta-mathematical entities. Roughly, an interpretation j of a theory T into a theory S (we write j : S¤T ) is a structure-preserving map, mapping axioms of T to theorems of S. Structurepreserving means ...
x - Loughborough University Intranet
... • Every theorem of a given deductive theory is satisfied by any model of the axiomatic system of this theory; moreover at every theorem one can associate a general logical statement logically provable that establishes that the considered theorem is satisfied in any model of this ...
... • Every theorem of a given deductive theory is satisfied by any model of the axiomatic system of this theory; moreover at every theorem one can associate a general logical statement logically provable that establishes that the considered theorem is satisfied in any model of this ...
Forking in simple theories and CM-triviality Daniel Palacín Cruz
... equivalence relations. Nevertheless, every theory with the strict order property has a hyperimaginary which is not eliminable [2]. Therefore, there are examples of small theories that do not eliminate hyperimaginaries; but the question is still open for small simple theories. In addition, there is a ...
... equivalence relations. Nevertheless, every theory with the strict order property has a hyperimaginary which is not eliminable [2]. Therefore, there are examples of small theories that do not eliminate hyperimaginaries; but the question is still open for small simple theories. In addition, there is a ...
Elements of Finite Model Theory
... although in recent years connections with other areas, such as formal methods and verification, and artificial intelligence, have been discovered. The birth of finite model theory is often identified with Trakhtenbrot’s result from 1950 stating that validity over finite models is not recursively enumerab ...
... although in recent years connections with other areas, such as formal methods and verification, and artificial intelligence, have been discovered. The birth of finite model theory is often identified with Trakhtenbrot’s result from 1950 stating that validity over finite models is not recursively enumerab ...
Proof Nets Sequentialisation In Multiplicative Linear Logic
... essentially to the one corresponding to subformula trees and to the one providing the axiom links. The key result in the theory of proof nets is the sequentialisation theorem, which states that it is possible to recover a sequent calculus derivation from a proof net. The standard proof of sequential ...
... essentially to the one corresponding to subformula trees and to the one providing the axiom links. The key result in the theory of proof nets is the sequentialisation theorem, which states that it is possible to recover a sequent calculus derivation from a proof net. The standard proof of sequential ...
Goal-directed Proof Theory
... [Girard 87]) has originated from the functional interpretation provided by the Curry-Howard's isomorphism between formulas and types in functional languages [Gabbay and DeQueiroz 92],[Wansing 90]. In parallel with the theoretical study of the logics mentioned above and their applications, there has ...
... [Girard 87]) has originated from the functional interpretation provided by the Curry-Howard's isomorphism between formulas and types in functional languages [Gabbay and DeQueiroz 92],[Wansing 90]. In parallel with the theoretical study of the logics mentioned above and their applications, there has ...
22c:145 Artificial Intelligence
... A logic is a triple !L, S, R" where L, the logic’s language, is a class of sentences described by a formal grammar. S , the logic’s semantics is a formal specification of how to assign meaning in the “real world” to the elements of L. R, the logic’s inference system, is a set of formal derivation ru ...
... A logic is a triple !L, S, R" where L, the logic’s language, is a class of sentences described by a formal grammar. S , the logic’s semantics is a formal specification of how to assign meaning in the “real world” to the elements of L. R, the logic’s inference system, is a set of formal derivation ru ...
Truth-Functional Logic
... A statement like A ∧ B ∨ C is ambiguous: is this the conjunction of A and B ∨ C, or is this a disjunction of A ∧ B and C? We will require that our statements are not ambiguous, and we will use parentheses to do so. So, if this statement was meant to be a conjunction of A and B ∨ C, we will write A ∧ ...
... A statement like A ∧ B ∨ C is ambiguous: is this the conjunction of A and B ∨ C, or is this a disjunction of A ∧ B and C? We will require that our statements are not ambiguous, and we will use parentheses to do so. So, if this statement was meant to be a conjunction of A and B ∨ C, we will write A ∧ ...
