Lesson 2
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Introduction to Logic ...
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Introduction to Logic ...
Overview of proposition and predicate logic Introduction
... Some technical names for this form of “follows from” are entailment, semantic consequence. Formulated somewhat sloppy, Σ |= ϕ says that in any world where the theory Σ holds, ϕ must also hold. Remark. The same remark as with substitution applies for the definition of semantics: for humans the meanin ...
... Some technical names for this form of “follows from” are entailment, semantic consequence. Formulated somewhat sloppy, Σ |= ϕ says that in any world where the theory Σ holds, ϕ must also hold. Remark. The same remark as with substitution applies for the definition of semantics: for humans the meanin ...
A preprint version is available here in pdf.
... Rep(M, N ) and SSy(M ), and that these two are contained in SSy(M, N ). Examples can be given (using the tools outlined in this section and in Section 4) for which these are all different. On the other hand if the pair (M, N ) is recursively saturated then SSy(M, N ) = SSy(M ). Note that SSy(M ) can ...
... Rep(M, N ) and SSy(M ), and that these two are contained in SSy(M, N ). Examples can be given (using the tools outlined in this section and in Section 4) for which these are all different. On the other hand if the pair (M, N ) is recursively saturated then SSy(M, N ) = SSy(M ). Note that SSy(M ) can ...
A Brief Introduction to the Intuitionistic Propositional Calculus
... the other point of view. If we can prove more classically than intuitionistically, we know more about a statement ϕ if we know it is intuitionistically valid than if it is (merely) classically valid. The particular utility of this “more that we know” became apparent with the rise of computers and th ...
... the other point of view. If we can prove more classically than intuitionistically, we know more about a statement ϕ if we know it is intuitionistically valid than if it is (merely) classically valid. The particular utility of this “more that we know” became apparent with the rise of computers and th ...
Quantified Equilibrium Logic and the First Order Logic of Here
... slightly different version of QEL where the so-called unique name assumption or UNA is not assumed from the outset but may be added as a special requirement for specific applications. The motivation for relaxing the UNA is to make equilibrium logic more flexible for certain kinds of applications. For i ...
... slightly different version of QEL where the so-called unique name assumption or UNA is not assumed from the outset but may be added as a special requirement for specific applications. The motivation for relaxing the UNA is to make equilibrium logic more flexible for certain kinds of applications. For i ...
BEYOND FIRST ORDER LOGIC: FROM NUMBER OF
... distinguish it from first order model theory. We give more detailed examples accessible to model theorists of all sorts. We conclude with questions about countable models which require only a basic background in logic. For the past 50 years most research in model theory has focused on first order lo ...
... distinguish it from first order model theory. We give more detailed examples accessible to model theorists of all sorts. We conclude with questions about countable models which require only a basic background in logic. For the past 50 years most research in model theory has focused on first order lo ...
Knowledge representation 1
... Logic: formal methods Logic is used by computer scientists when they are engaged in Formal Methods: describing the performance of a program precisely, so that they can prove that it does (or doesn’t) perform the task that it is supposed to. In other words, establishing the validity of a program. ...
... Logic: formal methods Logic is used by computer scientists when they are engaged in Formal Methods: describing the performance of a program precisely, so that they can prove that it does (or doesn’t) perform the task that it is supposed to. In other words, establishing the validity of a program. ...
Subintuitionistic Logics with Kripke Semantics
... G. Corsi, in [1], introduced sublogics of intuitionistic propositional logic IPC which are characterized by classes of Kripke models in which no assumption of truth preservation is made, and proved strong completeness for those systems. Her basic system was called F. G. Restall [4] made a similar st ...
... G. Corsi, in [1], introduced sublogics of intuitionistic propositional logic IPC which are characterized by classes of Kripke models in which no assumption of truth preservation is made, and proved strong completeness for those systems. Her basic system was called F. G. Restall [4] made a similar st ...
Truth in the limit
... Hilbert – evidently influenced by Kronecker – recalled the Aristotelian notions of actual and potential infinity (see [1]). Actually infinite sets simply contain infinitely many members. Potentially infinite sets are finite, but they allow arbitrary finite enlargements. These enlargements can be rep ...
... Hilbert – evidently influenced by Kronecker – recalled the Aristotelian notions of actual and potential infinity (see [1]). Actually infinite sets simply contain infinitely many members. Potentially infinite sets are finite, but they allow arbitrary finite enlargements. These enlargements can be rep ...
Chapter 1 Section 2
... observations and the knowledge base are consistent (i.e., satisfiable). The augmented knowledge base is clearly not consistent if the assumables are all true. The switches are both up, but the lights are not lit. Some of the assumables must then be false. This is the basis for the method to diagnose ...
... observations and the knowledge base are consistent (i.e., satisfiable). The augmented knowledge base is clearly not consistent if the assumables are all true. The switches are both up, but the lights are not lit. Some of the assumables must then be false. This is the basis for the method to diagnose ...
Beyond first order logic: From number of structures to structure of
... better describe certain key mathematical structures (e.g. the complex numbers with exponentiation), there has recently been a revival of ‘nonelementary model theory’. We develop contrasts between first order and non-elementary logic in a more detailed way than just noting ‘failure of compactness’. W ...
... better describe certain key mathematical structures (e.g. the complex numbers with exponentiation), there has recently been a revival of ‘nonelementary model theory’. We develop contrasts between first order and non-elementary logic in a more detailed way than just noting ‘failure of compactness’. W ...
Chapter 4, Mathematics
... multiplication are all algorithms. In logical theory ‘decision procedure’ is equivalent to ‘algorithm’. In cookery a reliable recipe is an algorithm for producing the soup, cake, stew or whatever it is that it tells us how to cook. A computer program, if it works, embodies some sort of algorithm. On ...
... multiplication are all algorithms. In logical theory ‘decision procedure’ is equivalent to ‘algorithm’. In cookery a reliable recipe is an algorithm for producing the soup, cake, stew or whatever it is that it tells us how to cook. A computer program, if it works, embodies some sort of algorithm. On ...
The Logic of Conditionals
... you can be sure that there is an FT-proof of Q from P1,…,Pn, even if you have not actually found such a proof. ...
... you can be sure that there is an FT-proof of Q from P1,…,Pn, even if you have not actually found such a proof. ...