Logic

Basic Concepts In Modal Logic by Edward N. Zalta

By Edward N. Zalta

Show description

Read Online or Download Basic Concepts In Modal Logic PDF

Best logic books

Technologically Enhanced Natural Radiation

This booklet on TENR discusses the fundamental Physics and Chemistry ideas of natural radiation. the present wisdom of the organic results of normal radiation is summarized. a wide selection of themes, from cosmic radiation to atmospheric, terrestrial and aquatic radiation is addressed, together with radon, thoron, and depleted uranium.

Computational Logic in Multi-Agent Systems: 13th International Workshop, CLIMA XIII, Montpellier, France, August 27-28, 2012. Proceedings

This publication constitutes the lawsuits of the thirteenth foreign Workshop on Computational common sense in Multi-Agent structures, CLIMA XIII, held in Montpellier, France, in August 2012. The eleven standard papers have been rigorously reviewed and chosen from 27 submissions and awarded with 3 invited papers. the aim of the CLIMA workshops is to supply a discussion board for discussing innovations, in accordance with computational good judgment, for representing, programming and reasoning approximately brokers and multi-agent platforms in a proper method.

Computational Logic in Multi-Agent Systems: 8th International Workshop, CLIMA VIII, Porto, Portugal, September 10-11, 2007. Revised Selected and Invited Papers

This e-book constitutes the completely refereed post-conference court cases of the eighth foreign Workshop on Computational good judgment for Multi-Agent platforms, CLIMA VIII, held in Porto, Portugal, in September 2007 - co-located with ICLP 2008, the overseas convention on common sense Programming. The 14 revised complete technical papers and 1 method description paper offered including 1 invited paper have been rigorously chosen from 33 submissions and went via a minimum of rounds of reviewing and development.

Logic and the Nature of God

The booklet '. .. might be guaranteed of the eye of the numerous on either side of the Atlantic who're fascinated about this topic. ' John Hick

Additional resources for Basic Concepts In Modal Logic

Sample text

4: Consistent and Maximal-Consistent Sets of Formulas Some readers may have already encountered the idea that a set of formulas Γ is consistent (relative to logic Σ) just in case there is no formula ϕ such that both ϕ and ¬ϕ are deducible from Γ (in Σ). But the following theorem shows this to be equivalent to saying that a set Γ is consistent (relative to Σ) just in case the falsum is not derivable from Γ (in Σ) 50) Theorem: Γ Σ⊥ iff there is a formula ϕ such that Γ Σϕ & ¬ϕ. Proof : By (45), given that ⊥ and ϕ & ¬ϕ are tautological consequences of each other.

This may come as a surprise. Moreover, it is a consequence that if ¦ϕ is taken as a primitive formula of the language rather than defined as ¬£¬ϕ, then in the definition of a normal logic we have to stipulate that normal logics, in addition to containing K and being closed under RN, contain all the instances of the valid schema ¦ϕ ↔ ¬£¬ϕ, for otherwise we could not preserve the interdefinability of the £ and ¦ in normal systems. Exercise 1 : Prove that if Σ is a normal logic, then Σ contains the following theorems and is closed under the following rules:17 ¦¬ϕ ↔ ¬£ϕ ϕ → ψ/£ϕ → £ψ (‘RM’) ϕ ↔ ψ/£ϕ ↔ £ψ (‘RE’) ϕ → (ψ → χ)/£ϕ → (£ψ → £χ) (‘RR’) £(ϕ & ψ) → (£ϕ & £ψ) (‘M’) (£ϕ & £ψ) → £(ϕ & ψ) (‘C’) £(ϕ & ψ) ↔ (£ϕ & £ψ) (‘R’) (ϕ1 & .

So by conditional proof, if M1 M1 |=w1 £ϕ, then |=w1 ϕ, which means, by the Remark in (7), that 1 |=M w1 £ϕ → ϕ. Now assume (ii). Then, by antecedent failure, M1 1 |=w1 £ϕ → ϕ. So, in either case, we have |=M w1 £ϕ → ϕ. 1 Proof of (b): By (a) and the Fact , we know |=M w2 £ϕ → ϕ. So since M1 £ϕ → ϕ is true in both w1 and w2 , we have |= £ϕ → ϕ. Since it is clear that RM1 is not reflexive, we have established that every instance of the T schema is true in M1 , but RM1 is not reflexive. This counterexample shows that the ‘converse’ of the present theorem is false.

Download PDF sample

Rated 4.73 of 5 – based on 12 votes