Chapter 2 Propositional Logic
... On the semantic conception, logical consequence amounts to: truth-preservation in virtue of the meanings of the logical constants. This slogan isn’t perfectly clear, but it does lead to a clearer thought: suppose we keep the meanings of an argument’s logical constants fixed, but vary everything else ...
... On the semantic conception, logical consequence amounts to: truth-preservation in virtue of the meanings of the logical constants. This slogan isn’t perfectly clear, but it does lead to a clearer thought: suppose we keep the meanings of an argument’s logical constants fixed, but vary everything else ...
Structural Logical Relations
... We shall prove that for every derivation of eτ , there exists a v τ , s.t. e −→∗ v and v ⇑ τ via a unary structural logical relation. The challenge, however, is the choice of a predicate P . It may come as a surprise that it is sufficient to characterize the fact that a term has a normal form withou ...
... We shall prove that for every derivation of eτ , there exists a v τ , s.t. e −→∗ v and v ⇑ τ via a unary structural logical relation. The challenge, however, is the choice of a predicate P . It may come as a surprise that it is sufficient to characterize the fact that a term has a normal form withou ...
logic for computer science - Institute for Computing and Information
... In the middle of the last century Boole laid down what we now see as the mathematical basis for computer hardware and propositional logic, but the logics that we are going to look at really started towards the end of the century with the work of Gottlob Frege, a German mathematician working in relat ...
... In the middle of the last century Boole laid down what we now see as the mathematical basis for computer hardware and propositional logic, but the logics that we are going to look at really started towards the end of the century with the work of Gottlob Frege, a German mathematician working in relat ...
Deep Sequent Systems for Modal Logic
... approaches. It allows to capture a wide class of modal logics and does so systematically. In many important cases it yields systems which are natural and easy to use, which have good structural properties like contractionadmissibility and invertibility of all rules, and which give rise to decision p ...
... approaches. It allows to capture a wide class of modal logics and does so systematically. In many important cases it yields systems which are natural and easy to use, which have good structural properties like contractionadmissibility and invertibility of all rules, and which give rise to decision p ...
Finite Presentations of Infinite Structures: Automata and
... necessarily finite structures such that the approach and methods of finite model theory make sense. There are two obvious and fundamental conditions : Finite representations. Every structure A ∈ D should be representable in a finite way (e.g. by a binary string, by an algorithm, by a collection of ...
... necessarily finite structures such that the approach and methods of finite model theory make sense. There are two obvious and fundamental conditions : Finite representations. Every structure A ∈ D should be representable in a finite way (e.g. by a binary string, by an algorithm, by a collection of ...
Predicate logic definitions
... important details dealt with by the formal semantics are left implicit. ...
... important details dealt with by the formal semantics are left implicit. ...
Inference in First
... 5. Eliminate existential quantification by introducing Skolem constants/functions (x)P(x) P(c) c is a Skolem constant (a brand-new constant symbol that is not used in any other sentence) (x)(y)P(x,y) becomes (x)P(x, f(x)) since is within the scope of a universally quantified variable, use a ...
... 5. Eliminate existential quantification by introducing Skolem constants/functions (x)P(x) P(c) c is a Skolem constant (a brand-new constant symbol that is not used in any other sentence) (x)(y)P(x,y) becomes (x)P(x, f(x)) since is within the scope of a universally quantified variable, use a ...
Decision procedures in Algebra and Logic
... a structure is an instance of that structure, regardless of how many other axioms that instance happens to have. For example, all groups are also semigroups and magmas. ...
... a structure is an instance of that structure, regardless of how many other axioms that instance happens to have. For example, all groups are also semigroups and magmas. ...
Introduction to Linear Logic
... For pedagogical purposes we shall also have a look at Classical Logic as well as Intuitionistic Logic. Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control. The focus of ...
... For pedagogical purposes we shall also have a look at Classical Logic as well as Intuitionistic Logic. Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control. The focus of ...
The Herbrand Manifesto
... There are benefits and disadvantages to doing things this way. On the one hand, with Herbrand semantics, we no longer have many of the nice features of Tarskian semantics compactness, inferential completeness, and semidecidability. On the other hand, there are some real benefits to Herbrand semantic ...
... There are benefits and disadvantages to doing things this way. On the one hand, with Herbrand semantics, we no longer have many of the nice features of Tarskian semantics compactness, inferential completeness, and semidecidability. On the other hand, there are some real benefits to Herbrand semantic ...
The substitutional theory of logical consequence
... to the nonlogical expressions plus the specification of a domain. There is another important difference: The model-theoretic analysis of validity relies on a set-theoretic definition of truth in a model. The substitutional account, in contrast, requires an ‘absolute’ notion of truth that is not rela ...
... to the nonlogical expressions plus the specification of a domain. There is another important difference: The model-theoretic analysis of validity relies on a set-theoretic definition of truth in a model. The substitutional account, in contrast, requires an ‘absolute’ notion of truth that is not rela ...
Programming with Classical Proofs
... These systems correspond to classical propositional logic, which means that their type systems are rather simple, and that, when they are equipped with datatypes, they are more closely related to real world computer programming languages than first-order systems are. But since we are interested in p ...
... These systems correspond to classical propositional logic, which means that their type systems are rather simple, and that, when they are equipped with datatypes, they are more closely related to real world computer programming languages than first-order systems are. But since we are interested in p ...
Nominal Monoids
... nominal sets were used to prove independence of the axiom of choice, and other axioms. In Computer Science, they have been rediscovered by Gabbay and Pitts in [7], as an elegant formalism for modeling name binding. Since then, nominal sets have become a lively topic in semantics. They were also inde ...
... nominal sets were used to prove independence of the axiom of choice, and other axioms. In Computer Science, they have been rediscovered by Gabbay and Pitts in [7], as an elegant formalism for modeling name binding. Since then, nominal sets have become a lively topic in semantics. They were also inde ...
A Logical Expression of Reasoning
... real science, they make more the exception than the rule, although they undoubtedly have the strong appeal of serving as a paradigm, a utopia every science should strive to achieve. This is the case of the so called social sciences, such as sociology and economy, but it is also the case of practical ...
... real science, they make more the exception than the rule, although they undoubtedly have the strong appeal of serving as a paradigm, a utopia every science should strive to achieve. This is the case of the so called social sciences, such as sociology and economy, but it is also the case of practical ...
John L. Pollock
... the predicate calculus is indispensable if for no other reason than that it is used so widely in the formulation of philosophical theories. This is partly because it has become conventional to formulate theories in that way, but it is also because the predicate calculus provides a medium for such fo ...
... the predicate calculus is indispensable if for no other reason than that it is used so widely in the formulation of philosophical theories. This is partly because it has become conventional to formulate theories in that way, but it is also because the predicate calculus provides a medium for such fo ...
Continuous Markovian Logic – From Complete ∗ Luca Cardelli
... where L is the set of logical formulas. However, the computability of D is sometimes problematic, as it is the computability of d(P, φ) for an infinite or extremely big process P and for this reason approximation techniques such as statistical model checking [15, 22] are used to evaluate d(P, φ) wit ...
... where L is the set of logical formulas. However, the computability of D is sometimes problematic, as it is the computability of d(P, φ) for an infinite or extremely big process P and for this reason approximation techniques such as statistical model checking [15, 22] are used to evaluate d(P, φ) wit ...
A sequent calculus demonstration of Herbrand`s Theorem
... We give first the definition of Herbrand proofs as formulated by Buss [2]. Remark 1. We consider, for cleanness of presentation, only pure first-order logic over a signature of relation symbols and function symbols, containing at least one constant symbol. Extending our approach to one dealing theor ...
... We give first the definition of Herbrand proofs as formulated by Buss [2]. Remark 1. We consider, for cleanness of presentation, only pure first-order logic over a signature of relation symbols and function symbols, containing at least one constant symbol. Extending our approach to one dealing theor ...
Logic 1 Lecture Notes Part I: Propositional Logic
... letters using explicit quotation marks, and you may have noticed that in many preceding cases we have omitted them. In such contexts, where it appears that the object language expression is being mentioned and hence quotation marks are technically called for, we adopt the liberating view that the ob ...
... letters using explicit quotation marks, and you may have noticed that in many preceding cases we have omitted them. In such contexts, where it appears that the object language expression is being mentioned and hence quotation marks are technically called for, we adopt the liberating view that the ob ...
LINEAR LOGIC AS A FRAMEWORK FOR SPECIFYING SEQUENT
... A1 and A2 . In other words, those subgoals immediately to the left of an ⇒ are attempted with empty bounded contexts: the bounded contexts, here ∆ and A, are divided up to be used to prove those goals immediately to the left of −◦. 2.3. Applications of Forum. Forum specifications have been presented ...
... A1 and A2 . In other words, those subgoals immediately to the left of an ⇒ are attempted with empty bounded contexts: the bounded contexts, here ∆ and A, are divided up to be used to prove those goals immediately to the left of −◦. 2.3. Applications of Forum. Forum specifications have been presented ...
Introduction to Logic
... be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth value” – either both are were false or both are true. Thus one obtains the idea that Two statemen ...
... be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth value” – either both are were false or both are true. Thus one obtains the idea that Two statemen ...
Model-Checking First-Order Logic Automata and Locality
... • Methods based on the locality of first-order logic. In the rest of this talk, we first review these two methods using the results on strings; graphs of bounded tree-width; and graphs of bounded degree. ...
... • Methods based on the locality of first-order logic. In the rest of this talk, we first review these two methods using the results on strings; graphs of bounded tree-width; and graphs of bounded degree. ...
Logic and Proof Jeremy Avigad Robert Y. Lewis Floris van Doorn
... From this perspective, logic is not so much a language for asserting truth, but a language for describing possible states of affairs. In other words, logic provides a specification language, with expressions that can be true or false depending on how we interpret the symbols that are allowed to vary. ...
... From this perspective, logic is not so much a language for asserting truth, but a language for describing possible states of affairs. In other words, logic provides a specification language, with expressions that can be true or false depending on how we interpret the symbols that are allowed to vary. ...
John Nolt – Logics, chp 11-12
... but I would still be the same person—namely, me. These ideas are reflected in the model introduced above. Object (3, for example, exists in w1 and w2. It therefore exhibits transworld identity. Moreover, it is in the extension of the predicate 'B' in wx, but not in w2. Thus, though it is the same ob ...
... but I would still be the same person—namely, me. These ideas are reflected in the model introduced above. Object (3, for example, exists in w1 and w2. It therefore exhibits transworld identity. Moreover, it is in the extension of the predicate 'B' in wx, but not in w2. Thus, though it is the same ob ...
Using linear logic to reason about sequent systems ?
... possible, and since contexts in Forum are either multisets or sets, we will not be able to represent sequents that make use of lists. It is unlikely, for example, that non-commutative object-logics can be encoded into our linear logic meta theory along the lines we describe below. ...
... possible, and since contexts in Forum are either multisets or sets, we will not be able to represent sequents that make use of lists. It is unlikely, for example, that non-commutative object-logics can be encoded into our linear logic meta theory along the lines we describe below. ...
Using linear logic to reason about sequent systems
... relevant here since the scope of ? will always be atomic. Lemma 1. If a sequent has a Forum proof, it has a proof in which there are no occurrences of decide? applied to an atomic formula. Proof Permute all occurrences of decide? involving an atomic formula up in a proof until they reach an instance ...
... relevant here since the scope of ? will always be atomic. Lemma 1. If a sequent has a Forum proof, it has a proof in which there are no occurrences of decide? applied to an atomic formula. Proof Permute all occurrences of decide? involving an atomic formula up in a proof until they reach an instance ...