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... 2. Mapping fJ: (TUF,V)n TUF,V assigned to every f F(n) with fJ(t1, ... , tn) : f(t1, ... , tn) A term interpretation I for F and consists of: 1. A term algebra for F 2. I TB,,F,V (set of atoms that are true; equivalently it can be seen as an assignment of a relation pI (TUF,V)n to every ...
... 2. Mapping fJ: (TUF,V)n TUF,V assigned to every f F(n) with fJ(t1, ... , tn) : f(t1, ... , tn) A term interpretation I for F and consists of: 1. A term algebra for F 2. I TB,,F,V (set of atoms that are true; equivalently it can be seen as an assignment of a relation pI (TUF,V)n to every ...
Tactics for Separation Logic Abstract Andrew W. Appel INRIA Rocquencourt & Princeton University
... proving an imperative program, much of the reasoning is not about memory cells but concerns the abstract mathematical objects that the program’s data structures represent. Lemmas about those objects are most conveniently proved in a general-purpose higher-order logic, especially when there are large ...
... proving an imperative program, much of the reasoning is not about memory cells but concerns the abstract mathematical objects that the program’s data structures represent. Lemmas about those objects are most conveniently proved in a general-purpose higher-order logic, especially when there are large ...
Modal Logic - Web Services Overview
... Revisited Now we have all background to illustrate solution to ...
... Revisited Now we have all background to illustrate solution to ...
chapter9
... can be proved • Entailment for FOPC is semi-decidable: algorithms exist that say yes to every entailed sentence, but no algorithm exists that also says no to every nonentailed sentence. • Our proof procedure could go on and on, generating more and more deeply nested terms, but we will not know wheth ...
... can be proved • Entailment for FOPC is semi-decidable: algorithms exist that say yes to every entailed sentence, but no algorithm exists that also says no to every nonentailed sentence. • Our proof procedure could go on and on, generating more and more deeply nested terms, but we will not know wheth ...
FC §1.1, §1.2 - Mypage at Indiana University
... many), and, in general, most of them are not particularly interesting. Until you have actually made the deduction, you don’t really know the conclusion, and knowing which of the possible chains of deduction to follow is not easy. The art of logic is to find an interesting conclusion and a chain of l ...
... many), and, in general, most of them are not particularly interesting. Until you have actually made the deduction, you don’t really know the conclusion, and knowing which of the possible chains of deduction to follow is not easy. The art of logic is to find an interesting conclusion and a chain of l ...
Using linear logic to reason about sequent systems
... The cut formula ⊥◦− bBc ◦− dBe is logically equivalent to dBe −◦ bBc⊥ . Taken together, we have (the not surprising fact) that left and right are duals of each other: dBe ≡ bBc⊥ . Of course, if the cut and initial rules involve some modals (as in intuitionistic or classical encodings of sequents), t ...
... The cut formula ⊥◦− bBc ◦− dBe is logically equivalent to dBe −◦ bBc⊥ . Taken together, we have (the not surprising fact) that left and right are duals of each other: dBe ≡ bBc⊥ . Of course, if the cut and initial rules involve some modals (as in intuitionistic or classical encodings of sequents), t ...
Document
... proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no maMer what proposi:ons are subs:tuted into its proposi:onal variables. • ...
... proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no maMer what proposi:ons are subs:tuted into its proposi:onal variables. • ...
Proof Theory of Finite-valued Logics
... calculi (Chapter 2), sequent calculi (Chapter 3), natural deduction (Chapter 4) and also tableaux can be represented; the recognition of a duality between two types— “negative” and “positive”—of resolution, sequents and tableaux (see also Baaz et al. [1993b]); bounds for partial normal forms for gen ...
... calculi (Chapter 2), sequent calculi (Chapter 3), natural deduction (Chapter 4) and also tableaux can be represented; the recognition of a duality between two types— “negative” and “positive”—of resolution, sequents and tableaux (see also Baaz et al. [1993b]); bounds for partial normal forms for gen ...
Deep Sequent Systems for Modal Logic
... pure systems for modal logics. This formalism is based on deep inference, which is the ability to apply rules deep inside of a formula. So far the calculus of structures has captured essentially those modal logics which can also be captured using the sequent calculus or hypersequents. In particular ...
... pure systems for modal logics. This formalism is based on deep inference, which is the ability to apply rules deep inside of a formula. So far the calculus of structures has captured essentially those modal logics which can also be captured using the sequent calculus or hypersequents. In particular ...
Proof theory for modal logic
... one interpretation, the necessity of A means that A holds in all circumstances, and the possibility of A means that A holds in some circumstances. The definability of possibility in terms of necessity is analogous to the classical definability of existence in terms of universality. The first axiomat ...
... one interpretation, the necessity of A means that A holds in all circumstances, and the possibility of A means that A holds in some circumstances. The definability of possibility in terms of necessity is analogous to the classical definability of existence in terms of universality. The first axiomat ...
An argumentation framework in default logic
... Of course, as Poole [13, p. 146] himself recognizes when discussing a similar example, for an argument to be preferred not only the final conclusion but also all intermediate conclusions must be preferred. The problem with definition 2.1, however, is that it does not recognize b as an intermediate c ...
... Of course, as Poole [13, p. 146] himself recognizes when discussing a similar example, for an argument to be preferred not only the final conclusion but also all intermediate conclusions must be preferred. The problem with definition 2.1, however, is that it does not recognize b as an intermediate c ...
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.