Algebraic Laws for Nondeterminism and Concurrency
... well developed in recent years [ 1, 111and applied successfullyto many nontrivial languages.Even languageswith parallel constructs have been treated in this way, using the power-domain constructions of [3], [7], and [lo]. Indeed for such languagesthere is no shortageof possibledenotational models. F ...
... well developed in recent years [ 1, 111and applied successfullyto many nontrivial languages.Even languageswith parallel constructs have been treated in this way, using the power-domain constructions of [3], [7], and [lo]. Indeed for such languagesthere is no shortageof possibledenotational models. F ...
THE SEMANTICS OF MODAL PREDICATE LOGIC II. MODAL
... more sophisticated notion of a modal individual and identity-at-a-world. It remains unsatisfactory having to choose between these competing semantics. Moreover, it would be nice if the difference between these semantics was better understood. Certainly, much research has been done into standard sema ...
... more sophisticated notion of a modal individual and identity-at-a-world. It remains unsatisfactory having to choose between these competing semantics. Moreover, it would be nice if the difference between these semantics was better understood. Certainly, much research has been done into standard sema ...
Chapter 9: Initial Theorems about Axiom System AS1
... if „α, and „α→β, then „β. The remaining occurrence of ‘→’ is under the predicate ‘„’; it is accordingly a proper noun referring to the conditional connective of the object language. When we translate ‘„’ as ‘is a theorem’, we obtain: if α is a theorem, and α→β is a theorem, then β is a theorem. The ...
... if „α, and „α→β, then „β. The remaining occurrence of ‘→’ is under the predicate ‘„’; it is accordingly a proper noun referring to the conditional connective of the object language. When we translate ‘„’ as ‘is a theorem’, we obtain: if α is a theorem, and α→β is a theorem, then β is a theorem. The ...
Plausibility structures for default reasoning
... satisfies (LLE), (RW) and (REF), i.e. that f is a mapping from L to U satisfying ϕ ∈ f (ϕ): (AND) f is a mapping from L to T. (OR) f (ϕ) ∩ f (ϕ0 ) ⊆ f (ϕ ∨ ϕ0 ). Most of these properties are well known. However, (CM) and (REF) are est motivated when (AND) holds. Since (AND) does not always hold, it ...
... satisfies (LLE), (RW) and (REF), i.e. that f is a mapping from L to U satisfying ϕ ∈ f (ϕ): (AND) f is a mapping from L to T. (OR) f (ϕ) ∩ f (ϕ0 ) ⊆ f (ϕ ∨ ϕ0 ). Most of these properties are well known. However, (CM) and (REF) are est motivated when (AND) holds. Since (AND) does not always hold, it ...
First-Order Proof Theory of Arithmetic
... This chapter discusses the proof-theoretic foundations of the first-order theory of the non-negative integers. This first-order theory of numbers, also called ‘first-order arithmetic’, consists of the first-order sentences which are true about the integers. The study of first-order arithmetic is imp ...
... This chapter discusses the proof-theoretic foundations of the first-order theory of the non-negative integers. This first-order theory of numbers, also called ‘first-order arithmetic’, consists of the first-order sentences which are true about the integers. The study of first-order arithmetic is imp ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete a ...
... of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete a ...
Intuitionistic and Modal Logic
... • Theorem For finite Γ, Γ ` IPC ϕ iff ϕ is valid in all finite Kripke models of Γ for IPC. • Proof. The proof can be done by filtration. We will not do that here. Or by reducing the whole discussion to the set of subformulas of Γ ∪ {ϕ} (a so-called adequate set, both in the definition of the (reduce ...
... • Theorem For finite Γ, Γ ` IPC ϕ iff ϕ is valid in all finite Kripke models of Γ for IPC. • Proof. The proof can be done by filtration. We will not do that here. Or by reducing the whole discussion to the set of subformulas of Γ ∪ {ϕ} (a so-called adequate set, both in the definition of the (reduce ...
An argumentation framework in default logic
... conclusions can be invalidated by adding new information to the premises. This kind of reasoning is motivated by the fact that in real life people do not always have sufficient information to make a safe step towards the conclusion; instead, they often jump to conclusions by applying general, defeas ...
... conclusions can be invalidated by adding new information to the premises. This kind of reasoning is motivated by the fact that in real life people do not always have sufficient information to make a safe step towards the conclusion; instead, they often jump to conclusions by applying general, defeas ...
Building explicit induction schemas for cyclic induction reasoning
... rules. A main result of [3,4] is that any LKID proof is convertible into a CLKIDω proof. However, the conversion in the other direction is only conjectured. In this paper, we present a procedure that builds dynamically explicit induction schemas from the structural analysis of CLKIDω proofs. Firstly ...
... rules. A main result of [3,4] is that any LKID proof is convertible into a CLKIDω proof. However, the conversion in the other direction is only conjectured. In this paper, we present a procedure that builds dynamically explicit induction schemas from the structural analysis of CLKIDω proofs. Firstly ...
AN ALGEBRAIC APPROACH TO SUBFRAME LOGICS. MODAL
... continuum many logics between wK4 and K4. It is relatively easy to prove the FMP for K4 by using the standard (transitive) filtration argument. It was shown in [2] that both wK4 and wK4T0 also have the FMP, but the proofs are much more involved than that for K4 (the reason being the technical diffic ...
... continuum many logics between wK4 and K4. It is relatively easy to prove the FMP for K4 by using the standard (transitive) filtration argument. It was shown in [2] that both wK4 and wK4T0 also have the FMP, but the proofs are much more involved than that for K4 (the reason being the technical diffic ...
Lecture 09
... j with 2 ≤ j ≤ k. To show that P(k + 1) must be true under this assumption, two cases need to be considered: • If k + 1 is prime, then P(k + 1) is true. • Otherwise, k + 1 is composite and can be written as the product of two positive integers a and b with 2 ≤ a ≤ b < k + 1. By the inductive hypothe ...
... j with 2 ≤ j ≤ k. To show that P(k + 1) must be true under this assumption, two cases need to be considered: • If k + 1 is prime, then P(k + 1) is true. • Otherwise, k + 1 is composite and can be written as the product of two positive integers a and b with 2 ≤ a ≤ b < k + 1. By the inductive hypothe ...
![CS 512, Spring 2017, Handout 05 [1ex] Semantics of Classical](http://s1.studyres.com/store/data/001902216_1-d85c63c8a0994ab9df7b1ab59a6b4141-300x300.png)
CS 512, Spring 2017, Handout 05 [1ex] Semantics of Classical
... Let Γ a (possibly infinite) set of propositional WFF’s. If, for every model/interpretation/valuation (i.e., assignment of truth values to prop atoms), it holds that: I ...
... Let Γ a (possibly infinite) set of propositional WFF’s. If, for every model/interpretation/valuation (i.e., assignment of truth values to prop atoms), it holds that: I ...
Logical Arguments - Computer Science, Stony Brook University
... • All statements in an argument, except the final one, are called premises • The final statement is called the conclusion • The key fact about a valid argument is that the truth of the conclusion must necessarily follow from the truth of the premises • One way to determine the validity of an argume ...
... • All statements in an argument, except the final one, are called premises • The final statement is called the conclusion • The key fact about a valid argument is that the truth of the conclusion must necessarily follow from the truth of the premises • One way to determine the validity of an argume ...
Sets, Logic, Computation
... consequence and the syntactic notion of provability give us two completely different ways to make precise the idea that a sentence may follow from some others. The soundness and completeness theorems link these two characterization. In particular, we will prove Gödel’s completeness theorem, which st ...
... consequence and the syntactic notion of provability give us two completely different ways to make precise the idea that a sentence may follow from some others. The soundness and completeness theorems link these two characterization. In particular, we will prove Gödel’s completeness theorem, which st ...
John L. Pollock
... and techniques without becoming embroiled in unnecessary technical details. The most valuable technical tools are those provided by set theory and the predicate calculus. Knowledge of the predicate calculus is indispensable if for no other reason than that it is used so widely in the formulation of ...
... and techniques without becoming embroiled in unnecessary technical details. The most valuable technical tools are those provided by set theory and the predicate calculus. Knowledge of the predicate calculus is indispensable if for no other reason than that it is used so widely in the formulation of ...