Relevant Logic A Philosophical Examination of Inference Stephen Read February 21, 2012
... strange formal notions in its analysis of the intensional operators. Among various attempts to give these formal semantic notions some intuitive feel, two have come to be known as the American and Australian plans, the former proposing two new ’truth-values’, Both and Neither (that is, both and neit ...
... strange formal notions in its analysis of the intensional operators. Among various attempts to give these formal semantic notions some intuitive feel, two have come to be known as the American and Australian plans, the former proposing two new ’truth-values’, Both and Neither (that is, both and neit ...
CHAPTER 1. SENTENTIAL LOGIC 1. Introduction In sentential logic
... • If 7 is not odd then 2 is odd • If 7 is odd and 2 is odd then 2 is not prime • (7 is odd and 2 is odd) or 2 is prime We have improved on English in the last example by using parentheses to resolve an ambiguity. And, or, not, if . . . then (or implies) are called (sentential) connectives. Using the ...
... • If 7 is not odd then 2 is odd • If 7 is odd and 2 is odd then 2 is not prime • (7 is odd and 2 is odd) or 2 is prime We have improved on English in the last example by using parentheses to resolve an ambiguity. And, or, not, if . . . then (or implies) are called (sentential) connectives. Using the ...
Continuous first order logic and local stability
... Yet, continuous first order logic has significant advantages over earlier formalisms for metric structures. To begin with, it is an immediate generalisation of classical first order logic, more natural and less technically involved than previous formalisms. More importantly, it allows us to beat the ab ...
... Yet, continuous first order logic has significant advantages over earlier formalisms for metric structures. To begin with, it is an immediate generalisation of classical first order logic, more natural and less technically involved than previous formalisms. More importantly, it allows us to beat the ab ...
Review - UT Computer Science
... There are interesting first-order theories that are both consistent and complete with respect to particular interpretations of interest. One example is Presburger arithmetic, in which the universe is the natural numbers and there is a single function, plus, whose properties are axiomatized. There ar ...
... There are interesting first-order theories that are both consistent and complete with respect to particular interpretations of interest. One example is Presburger arithmetic, in which the universe is the natural numbers and there is a single function, plus, whose properties are axiomatized. There ar ...
The History of Categorical Logic
... with higher-order logic and type theories. Both Lawvere and Tierney were aiming at an elementary, that is first-order, axiomatic presentation of what are now called Grothendieck toposes, a special type of categories introduced by Alexandre Grothendieck in the context of algebraic geometry and sheaf ...
... with higher-order logic and type theories. Both Lawvere and Tierney were aiming at an elementary, that is first-order, axiomatic presentation of what are now called Grothendieck toposes, a special type of categories introduced by Alexandre Grothendieck in the context of algebraic geometry and sheaf ...
1Propositional Logic - Princeton University Press
... means without prior written permission of the publisher. ...
... means without prior written permission of the publisher. ...
The substitutional theory of logical consequence
... from the model-theoretic definition of logical consequence, because the universal quantifier over interpretations in the definition ranges over all models in the technical sense; but the ‘intended interpretation’ is not one of these models and cannot easily be identified with one of these models. M ...
... from the model-theoretic definition of logical consequence, because the universal quantifier over interpretations in the definition ranges over all models in the technical sense; but the ‘intended interpretation’ is not one of these models and cannot easily be identified with one of these models. M ...
In terlea v ed
... programs on a single processor (see e.g. [2]). In a popular formal model concurrency is represented by interleaving . This means that parallel processes are never executed at precisely the same instant, but take turns in executing atomic transitions. When one of the participating processes executes ...
... programs on a single processor (see e.g. [2]). In a popular formal model concurrency is represented by interleaving . This means that parallel processes are never executed at precisely the same instant, but take turns in executing atomic transitions. When one of the participating processes executes ...
Deep Sequent Systems for Modal Logic
... classes: labelled formalisms, which incorporate Kripke semantics in the proof system, and unlabelled formalisms, which do not. Prominent examples of unlabelled formalisms are the hypersequent calculus [1] and the display calculus [2, 10]. These and more can be found in the survey by Wansing [11]. A ...
... classes: labelled formalisms, which incorporate Kripke semantics in the proof system, and unlabelled formalisms, which do not. Prominent examples of unlabelled formalisms are the hypersequent calculus [1] and the display calculus [2, 10]. These and more can be found in the survey by Wansing [11]. A ...
Modular Construction of Complete Coalgebraic Logics
... property which ensures that combined logics have the Hennessy-Milner property w.r.t. behavioural equivalence, that is, the logical equivalence of states coincides with behavioural equivalence. Since this property is present in all of the basic constructs and is preserved by each combination of const ...
... property which ensures that combined logics have the Hennessy-Milner property w.r.t. behavioural equivalence, that is, the logical equivalence of states coincides with behavioural equivalence. Since this property is present in all of the basic constructs and is preserved by each combination of const ...
The Arithmetical Hierarchy Math 503
... sets according to some property, usually akin to complexity. A prototypical example is the cumulative hierarchy of set theory, which contains sets of ever-increasing size built up from smaller sets via the operations of power set and union. In recursion theory, the sets of immediate interest are tho ...
... sets according to some property, usually akin to complexity. A prototypical example is the cumulative hierarchy of set theory, which contains sets of ever-increasing size built up from smaller sets via the operations of power set and union. In recursion theory, the sets of immediate interest are tho ...
Studying Sequent Systems via Non-deterministic Multiple
... the cut-free fragment of LK, and provided semantics for this fragment using (non-deterministic) three-valued valuations.† Together with better understanding of the semantic role of the cut rule, this three-valued semantics was applied for proving several generalizations of the cut-elimination theore ...
... the cut-free fragment of LK, and provided semantics for this fragment using (non-deterministic) three-valued valuations.† Together with better understanding of the semantic role of the cut rule, this three-valued semantics was applied for proving several generalizations of the cut-elimination theore ...
FC §1.1, §1.2 - Mypage at Indiana University
... mulas themselves. But it is the applications that bring the subject to life for most people. We will, of course, cover some applications as we go along. In a sense, though, the real applications of logic include much of computer science and of mathematics itself. Among the fundamental elements of th ...
... mulas themselves. But it is the applications that bring the subject to life for most people. We will, of course, cover some applications as we go along. In a sense, though, the real applications of logic include much of computer science and of mathematics itself. Among the fundamental elements of th ...