Chapter 5 - Stanford Lagunita
... P and Q are clearly consequences of this conjunction, because there is no way for the conjunction to be true without each conjunct being true. Thus, we ...
... P and Q are clearly consequences of this conjunction, because there is no way for the conjunction to be true without each conjunct being true. Thus, we ...
SEQUENT SYSTEMS FOR MODAL LOGICS
... instance, by Hacking [1994]. Following Hacking, if introduction rules are to be regarded as defining logical operations, these rules must be such that the structural rules monotonicity (also called weakening, thinning, or dilution), reflexivity, and cut can be eliminated. Hacking claims that [i]t is ...
... instance, by Hacking [1994]. Following Hacking, if introduction rules are to be regarded as defining logical operations, these rules must be such that the structural rules monotonicity (also called weakening, thinning, or dilution), reflexivity, and cut can be eliminated. Hacking claims that [i]t is ...
A System of Interaction and Structure
... deep reasons for this kind of logic not to be expressible in the sequent calculus, and there is a simple formalism, which we call the calculus of structures, that is instead able to express self-dual non-commutativity with great ease. In fact, self-dual non-commutative operators naturally generate a ...
... deep reasons for this kind of logic not to be expressible in the sequent calculus, and there is a simple formalism, which we call the calculus of structures, that is instead able to express self-dual non-commutativity with great ease. In fact, self-dual non-commutative operators naturally generate a ...
The Foundations
... It is the foundation for expressing formal proofs in all branches of mathematics. ...
... It is the foundation for expressing formal proofs in all branches of mathematics. ...
CHAPTER 10 Gentzen Style Proof Systems for Classical Logic 1
... Gentzen systems reverse this situation by emphasizing the importance of inference rules, reducing the role of logical axioms to an absolute minimum. They may be less intuitive then the Hilbert-style systems, but they will allow us to give an effective automatic procedure for proof search, what was i ...
... Gentzen systems reverse this situation by emphasizing the importance of inference rules, reducing the role of logical axioms to an absolute minimum. They may be less intuitive then the Hilbert-style systems, but they will allow us to give an effective automatic procedure for proof search, what was i ...
PDF (216 KB)
... Constructive mathematics is interesting in Computer Science because of program correctness issues. There are several approaches to constructivism (see [4,5,19] for an overview). We are especially interested in the constructive recursive mathematics (CRM) approach developed by Markov [12,13] and in c ...
... Constructive mathematics is interesting in Computer Science because of program correctness issues. There are several approaches to constructivism (see [4,5,19] for an overview). We are especially interested in the constructive recursive mathematics (CRM) approach developed by Markov [12,13] and in c ...
Beginning Logic - University of Notre Dame
... we compare the sizes of the set of counting numbers 1, 2, 3, . . . and the set of real numbers between 0 and 1? Cantor developed a way to compare these sets and then gave a surprising construction to show that the set of real numbers is larger. Cantor’s idea, diagonalization, has been used in many o ...
... we compare the sizes of the set of counting numbers 1, 2, 3, . . . and the set of real numbers between 0 and 1? Cantor developed a way to compare these sets and then gave a surprising construction to show that the set of real numbers is larger. Cantor’s idea, diagonalization, has been used in many o ...
The Foundations
... A language(Vocabulary) for expressing them. A concise notation(Syntax) for writing them. A methodology for objectively reasoning about their truth or falsity (Semantics and Axiomatics). It is the foundation for expressing formal proofs in all branches of mathematics. ...
... A language(Vocabulary) for expressing them. A concise notation(Syntax) for writing them. A methodology for objectively reasoning about their truth or falsity (Semantics and Axiomatics). It is the foundation for expressing formal proofs in all branches of mathematics. ...
File
... pronouns for nouns in English grammar or multiple name substitution. Unfortunately, in most of the Mathematical writings (books or articles) the difference is not given explicity, the reader has to distinguish the name and object according to the context. This kind of catastrophic events occurs whil ...
... pronouns for nouns in English grammar or multiple name substitution. Unfortunately, in most of the Mathematical writings (books or articles) the difference is not given explicity, the reader has to distinguish the name and object according to the context. This kind of catastrophic events occurs whil ...
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 Hoare Logic for Linear Systems - School of Electronic Engineering
... aspects of the model then providing the requirements for a formal software development process. Widely used tools such as Simulink allow systems to be expressed as a signal flow graph formed by wiring together primitive components to form subsystems in a hierarchic fashion. Such tools support valida ...
... aspects of the model then providing the requirements for a formal software development process. Widely used tools such as Simulink allow systems to be expressed as a signal flow graph formed by wiring together primitive components to form subsystems in a hierarchic fashion. Such tools support valida ...
AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... For that purpose Kanger introduced the notions of a primary valuation and a system. A primary valuation for a language L of quantified modal logic is a function v which for every non-empty domain D assigns an appropriate extension in D to every individual constant, individual variable, and predicate ...
... For that purpose Kanger introduced the notions of a primary valuation and a system. A primary valuation for a language L of quantified modal logic is a function v which for every non-empty domain D assigns an appropriate extension in D to every individual constant, individual variable, and predicate ...
Proof Theory: From Arithmetic to Set Theory
... The natural deduction calculus and the sequent calculus were both invented by Gentzen in 1934. Both calculi are pretty illustrations of the symmetries of logic. In this course I shall focus on the sequent calculus since it is a central tool in ordinal analysis and allows for generalizations to infin ...
... The natural deduction calculus and the sequent calculus were both invented by Gentzen in 1934. Both calculi are pretty illustrations of the symmetries of logic. In this course I shall focus on the sequent calculus since it is a central tool in ordinal analysis and allows for generalizations to infin ...
Relevant Logic A Philosophical Examination of Inference Stephen Read February 21, 2012
... that disjunction is ambiguous. Further reflection on conjunction shows that it exhibits an ambiguity matching that discovered for disjunction. The intensional sense of conjunction so discerned (we call it, ‘fusion’) allows a suitable revision to the Classical Account of Validity and also to the Dedu ...
... that disjunction is ambiguous. Further reflection on conjunction shows that it exhibits an ambiguity matching that discovered for disjunction. The intensional sense of conjunction so discerned (we call it, ‘fusion’) allows a suitable revision to the Classical Account of Validity and also to the Dedu ...
A Critique of the Foundations of Hoare-Style
... This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for ...
... This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for ...
Proof Theory for Propositional Logic
... particular the fact that a conditional is counted as true whenever the antecedent (the first term, above) is false. Again, let’s just get comfortable doing the proofs for now. When we do truth tables we will discuss why this is the case for propositional logic. In both cases, the problem reveals f ...
... particular the fact that a conditional is counted as true whenever the antecedent (the first term, above) is false. Again, let’s just get comfortable doing the proofs for now. When we do truth tables we will discuss why this is the case for propositional logic. In both cases, the problem reveals f ...
A Critique of the Foundations of Hoare-Style Programming Logics
... This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for ...
... This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for ...
A joint logic of problems and propositions, a modified BHK
... Surprisingly, the calculus of problems coincides in form with Brouwer’s intuitionistic logic, as recently formalized by Heyting. [In fact, we shall argue] that [intuitionistic logic] should be replaced with the calculus of problems, since its objects are in reality not theoretical propositions but r ...
... Surprisingly, the calculus of problems coincides in form with Brouwer’s intuitionistic logic, as recently formalized by Heyting. [In fact, we shall argue] that [intuitionistic logic] should be replaced with the calculus of problems, since its objects are in reality not theoretical propositions but r ...
Algebraic foundations for the semantic treatment of inquisitive content
... arise. The first question is whether propositions should really be defined as arbitrary sets of possibilities, or whether we should adopt certain constraints on which sets of possibilities form suitable propositions and which don’t. The above discussion indicates that sets of possibilities are suffi ...
... arise. The first question is whether propositions should really be defined as arbitrary sets of possibilities, or whether we should adopt certain constraints on which sets of possibilities form suitable propositions and which don’t. The above discussion indicates that sets of possibilities are suffi ...
The Foundations
... A language(Vocabulary) for expressing them. A concise notation(Syntax) for writing them. A methodology for objectively reasoning about their truth or falsity (Semantics and Axiomatics). It is the foundation for expressing formal proofs in all branches of mathematics. ...
... A language(Vocabulary) for expressing them. A concise notation(Syntax) for writing them. A methodology for objectively reasoning about their truth or falsity (Semantics and Axiomatics). It is the foundation for expressing formal proofs in all branches of mathematics. ...
Mathematical Logic Fall 2004 Professor R. Moosa Contents
... Mathematical Logic is the study of the type of reasoning done by mathematicians. (i.e. proofs, as opposed to observation) Axioms are the first unprovable laws. They are statements about certain “basic concepts” (undefined first concepts). There is usually some sort of “soft” justification for believ ...
... Mathematical Logic is the study of the type of reasoning done by mathematicians. (i.e. proofs, as opposed to observation) Axioms are the first unprovable laws. They are statements about certain “basic concepts” (undefined first concepts). There is usually some sort of “soft” justification for believ ...
Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e
... does not provide a nonmonotonic logic, while S5 models of minimal knowledge have a natural interpretation as maximal sets of possible worlds. The goal of our work1 is to study the family of ground logics, from the semantical, computational and epistemological viewpoint. With respect to the first iss ...
... does not provide a nonmonotonic logic, while S5 models of minimal knowledge have a natural interpretation as maximal sets of possible worlds. The goal of our work1 is to study the family of ground logics, from the semantical, computational and epistemological viewpoint. With respect to the first iss ...