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In [[modal logic]], '''Sahlqvist formulas''' are a certain kind of modal formula with remarkable properties. The '''Sahlqvist correspondence theorem''' states that every Sahlqvist formula is [[Kripke semantics#Canonical models|canonical]], and corresponds to a [[first-order logic|first-order]] definable class of [[Kripke semantics|Kripke frames]].
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Sahlqvist's definition characterizes a decidable set of modal formulas with first-order correspondents. Since it is undecidable, by Chagrova's theorem, whether an arbitrary modal formula has a first-order correspondent, there are formulas with first-order frame conditions that are not Sahlqvist [Chagrova 1991] (see the examples below). Hence Sahlqvist formulas define only a (decidable) subset of modal formulas with first-order correspondents.
 
== Definition ==
Sahlqvist formulas are built up from implications, where the consequent is ''positive'' and the antecedent is of a restricted form.
* A ''boxed atom'' is a propositional atom preceded by a number (possibly 0) of boxes, i.e. a formula of the form <math>\Box\cdots\Box p</math> (often abbreviated as <math>\Box^i p</math> for <math>0 \leq i < \omega</math>).
* A ''Sahlqvist antecedent'' is a formula constructed using ∧, ∨, and <math>\Diamond</math> from boxed atoms, and negative formulas (including the constants ⊥, ⊤).
* A ''Sahlqvist implication'' is a formula ''A'' → ''B'', where ''A'' is a Sahlqvist antecedent, and ''B'' is a positive formula.
* A ''Sahlqvist formula'' is constructed from Sahlqvist implications using ∧ and <math>\Box</math> (unrestricted), and using ∨ on formulas with no common variables.
 
== Examples of Sahlqvist formulas ==
; <math>p \rightarrow \Diamond p</math>
: Its first-order corresponding formula is <math>\forall x \; Rxx</math>, and it defines all '''[[Reflexive relation|reflexive frames]]'''
; <math>p \rightarrow \Box\Diamond p</math>
: Its first-order corresponding formula is <math>\forall x \forall y [Rxy \rightarrow Ryx]</math>, and it defines all '''[[Symmetric relation|symmetric frames]]'''
; <math>\Diamond \Diamond p \rightarrow \Diamond p</math> or <math>\Box p \rightarrow \Box \Box p</math>
: Its first-order corresponding formula is <math>\forall x \forall y \forall z [(Rxy \land Ryz) \rightarrow Rxz]</math>, and it defines all '''[[Transitive relation|transitive frames]]'''
; <math>\Diamond p \rightarrow \Diamond \Diamond p</math> or <math>\Box \Box p \rightarrow \Box p</math>
: Its first-order corresponding formula is <math>\forall x \forall y [Rxy \rightarrow \exists z (Rxz \land Rzy)]</math>, and it defines all '''[[Dense order|dense frames]]'''
; <math>\Box p \rightarrow \Diamond p</math>
: Its first-order corresponding formula is <math>\forall x \exists y \; Rxy</math>, and it defines all '''right-unbounded frames''' (also called serial)
; <math>\Diamond\Box p \rightarrow \Box\Diamond p</math>
: Its first-order corresponding formula is <math>\forall x \forall x_1 \forall z_0 [Rxx_1 \land Rxz_0 \rightarrow \exists z_1 (Rx_1z_1 \land Rz_0z_1)]</math>, and it is the [[Church–Rosser theorem|Church-Rosser property]].
 
==Examples of non-Sahlqvist formulas==
; <math>\Box\Diamond p \rightarrow \Diamond \Box p</math>
: This is the ''McKinsey formula''; it does not have a first-order frame condition.
<math>\Box(\Box p \rightarrow p) \rightarrow \Box p</math>
: The ''Löb axiom'' is not Sahlqvist; again, it does not have a first-order frame condition.
; <math>(\Box\Diamond p \rightarrow \Diamond \Box p) \land (\Diamond\Diamond q \rightarrow \Diamond q)</math>
: The conjunction of the McKinsey formula and the (4) axiom has a first-order frame condition but is not equivalent to any Sahlqvist formula.
 
== Kracht's theorem ==
When a Sahlqvist formula is used as an axiom in a normal modal logic, the logic is guaranteed to be complete with respect to the elementary class of frames the axiom defines. This result comes from the Sahlqvist completeness theorem [Modal Logic, Blackburn ''et al.'', Theorem 4.42]. But there is also a converse theorem, namely a theorem that states which first-order conditions are the correspondents of Sahlqvist formulas. Kracht's theorem states that ''any Sahlqvist formula locally corresponds to a Kracht formula; and conversely, every Kracht formula is a local first-order correspondent of some Sahlqvist formula which can be effectively obtained from the Kracht formula'' [Modal Logic, Blackburn ''et al.'', Theorem 3.59].
 
==References==
 
* L. A. Chagrova, 1991. An undecidable problem in correspondence theory. ''Journal of Symbolic Logic'' 56:1261-1272.
* Marcus Kracht, 1993. How completeness and correspondence theory got married. In de Rijke, editor, ''Diamonds and Defaults'', pages 175-214.  Kluwer.
* Henrik Sahlqvist, 1975.  Correspondence and completeness in the first- and second-order semantics for modal logic.  In ''Proceedings of the Third Scandinavian Logic Symposium''.  North-Holland, Amsterdam.
 
[[Category:Modal logic]]

Revision as of 11:16, 4 March 2014

Pioneer Training & Consultancy Pte Ltd is an Approved Course Supplier (ACP) appointed by the Council for Estate Agencies (CEA) to conduct the Real Property Salesperson (RES) Course. A person aspiring to be actual property salespersons must cross the CEA's Real Estate (RES) examination or have equal qualification. This is among the registration criteria administered by Council for Estate Companies (CEA)

The principle cause many think that they will do it with out a actual estate agent is as a result of they suppose they'll come into an settlement with the client with out having to pay any form of commission. Nevertheless, this only means extra hassle and dangers to allow your property to be scouted by many trespassers. Moreover, when an agent is hired, it's easier to be able to consider any each day actions that spending time on commonly in search of shoppers to purchase/lease the property.

Region Property Consultancy & Management Providers Pte Ltd Citiprop Property Administration Pte Ltd Knight Frank Property Network KF Property Community Pte Ltd Yong An Park (D09) – Condominium For Hire The Glyndebourne (D11) – Condominium For Lease Scotts 28 (D09) – Condominium For Rent Condominium For Hire – The Balmoral (D10) Pretty house within the east, close to MRT Casa Merah (D16) – new condo launches singapore For Hire Very spacious residence near international faculty Condo For Hire – Leonie Towers (D09) GETTING YOUR PROPERTY OFFERED / LEASED? My point? Primarily based on my expertise and what I've noticed, investing in property is the commonest way for the average person to build up a big quantity of wealth However isn't it dangerous to invest in property now? Property Rotating Banner with Results

Have handed an trade examination i.e Frequent Examination for Home Agents (CEHA) or Real Property Company (REA) exam, or equal; Exclusive brokers are extra willing to share listing info thus guaranteeing the widest potential coverage inside the true property group via A number of Listings and Networking. Accepting a severe provide is less complicated since your agent is absolutely aware of all advertising exercise related with your property. This reduces your having to test with several brokers for any other affords. Worth control is definitely achieved. Paint work in good restore-discuss along with your Property Advisor if main works are nonetheless to be finished. Softening in residential property prices continue, led by 2.eight per cent decline in the index for Rest of Central Area

According to a Channel News Asia report, dated 30 Jan 2012, the number of agents in 2011 was 34,300. Based mostly on the current analysis from propwise.sg , the total commission generated by the actual property industry would quantity to about $785 million. You can simply calculated that average commission every agent would get is just about $22,886 (or about $1,907 per month). For leases lower than S$2500, agents normally cost both the tenants and the landlords a letting commission fee of half a month's rental. Our commitment to offering the best environment for patrons, sellers and actual estate professionals alike, will assist you to successfully negotiate by means of each side of a property transaction. Please wait for your turn, All the time Full Home. View Properties

Those are prime 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some essential documents that you must undergo the IRAS, so your software might be approved rapidly. This PIC grant permits you to develop your property company company from the tax deduction or cash payout options. Her profession took her to Germany, U.K. and varied Asian nations. Working with multi-national companies (e.g. Sony Ericsson) and colleges (e.g. German College Singapore) made sensitive in the direction of the wants and emotions of of people of varied ages and cultures, combined with the skill to establish optimistic relationships with families and other professionals. Southeast Asia Property Review - MarketPulse Q1 2014 Browse Brokers by First Title

That is our motto for our property management line of business. A effectively maintained estate holds its funding worth for the homeowners and is a snug place. Neighbour relations are typically good and homeowners discover the estate a welcome after a hard day's work. All these are solely doable if the estate is run by knowledgeable crew, a robust and visionary Management Council, an expert and competent Managing Agent and meticulous supporting groups just like the cleaning group, safety and technical group.