Proof Theory Sample Clauses

Proof Theory. Many presentations of separation logic are based on a model-theoretic logical conse- quence. We, instead, define logical consequence proof-theoretically. This gives our sys- tem an algorithmic flavour, similar to recent static assertion checkers for fragments of separation logic [2,9] that are built upon proof-theoretic decision procedures7. Γ ; v; F¯ € G from v’s point of view, G is a logical consequence of the *-conjunction of F¯ Γ ; v € F from v’s point of view, F is an axiom In the former judgment, F¯ is a multiset of formulas. The parameter v represents the current receiver, which is needed to determine the scope of predicate definitions. The logical consequence judgment is driven by standard natural deduction rules that are common to the logic of bunched implications [23] and linear logic [30]. These rules are detailed in [16]. We admit weakening, because Java is a garbage-collected language. The link between Γ ; v; F¯ € G and the axiom judgment Γ ; v € F is established by the following rule. (We omit the definitions of typing judgments Γ € v : T and Γ € F : ¤.) 7 Unfortunately, these fragments do not include -*, as needed for our iterator implementation. Γ ; v € G Γ € v : Object Γ € F¯ , G : ¤ Γ ; v; F¯ € G We now define the complete set of axioms. First, we repeat the split/merge law: Γ ; v € PointsTo(e. f , π, ej) *-* (PointsTo(e. f , π , ej)* PointsTo(e. f , π , ej)) Γ ; v € Perm(e.join, π) *-* (Perm(e.join, π )* Perm(e.join, π )) For the following axioms, recall that “F assures G” abbreviates “F -* (F * G)”. Γ ; v € true Γ ; v € false -* F Γ ; v € (e & F) -* (e * F) Γ ; v € (PointsTo(e. f , x, ej) & PointsTo(e. f , πj, ejj)) assures ej == ejj (Γ € e, ej : T ∧ Γ, x : T € F : ¤) ⇒ Γ ; v € (F[e/x]* e == ej) -* F[ej/x] The third of these axioms implies that boolean expressions are copyable: e -* (e * e). The following axiom lifts semantic validity of boolean expressions (which we do not axiomatize) to our proof theory: (Γ |= !e1 | !e2 | ej) ⇒ Γ ; v € (e1 * e2) -* ej The next axiom allows to apply class axioms. Here, axiom(t<π¯ j>) is the *-conjunction of all class axioms in t<π¯ j> and its supertypes.
Sample 1
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Related to Proof Theory

  • Non-Grievability No dispute over a claim for any benefits extended by this Health and Welfare Fund shall be subject to the grievance procedure.

  • Grievability Denial of a petition for reinstatement is grievable. The grievance may not be based on information other than that shared with the Employer at the time of the petition for reinstatement.

  • Proof of Sickness Sick leave with pay is only payable because of sickness or injury and employees who are absent from duty because of sickness may be required by the Employer to prove sickness. Failure to meet this requirement can be cause for disciplinary action. Repeated failure to meet this requirement can lead to dismissal. A doctor’s certificate may be requested for each leave of more than three (3) consecutive work days.

  • PROOF OF LICENSE The Contractor must provide to each Licensee who places a Purchase Order either: (i) the Product developer’s certified License Confirmation Certificates in the name of such Licensee; or (ii) a written confirmation from the Proprietary owner accepting Product invoice as proof of license. Contractor shall submit a sample certificate, or alternatively such written confirmation from the proprietary developer. Such certificates must be in a form acceptable to the Licensee.

  • Breach for Lack of Proof of Coverage The failure to comply with the requirements of this section at any time during the term of the Contract shall be considered a breach of the terms of the Contract and shall allow the People of the State of New York, the New York State Office of General Services, any entity authorized by law or regulation to use the Contract and their officers, agents, and employees to avail themselves of all remedies available under the Contract or at law or in equity.

  • Proof of WSIA Coverage Unless the HSP puts into effect and maintains Employers Liability and Voluntary Compensation as set out above, the HSP will provide the Funder with a valid Workplace Safety and Insurance Act, 1997 (“WSIA”) Clearance Certificate and any renewal replacements, and will pay all amounts required to be paid to maintain a valid WSIA Clearance Certificate throughout the term of this Agreement.

  • Proof of Illness A Board may request medical confirmation of illness or injury and any restrictions or limitations any Employee may have, confirming the dates of absence and the reason thereof (omitting a diagnosis). Medical confirmation is required to be provided by the Employee for absences of five (5) consecutive working days or longer. The medical confirmation may be required to be provided on a form prescribed by the Board. Where an Employee does not provide medical confirmation as requested, or otherwise declines to participate and/or cooperate in the administration of the Sick Leave Benefit Plan, access to compensation may be suspended or denied. Before access to compensation is denied, discussion will occur between the Union and the school board. Compensation will not be denied for the sole reason that the medical practitioner refuses to provide the required medical information. A school Board may require an independent medical examination to be completed by a medical practitioner qualified in respect of the illness or injury of the Board’s choice at the Board’s expense. In cases where the Employee’s failure to cooperate is the result of a medical condition, the Board shall consider those extenuating circumstances in arriving at a decision.

  • Investigation of Grievances The investigation of grievances shall not interfere with the orderly process of education in District 281.

  • Filing a Grievance Grievances may be filed by the Union on behalf of an employee or on behalf of a group of employees. If the Union does so, it will set forth the name of the employee or the names of the group of employees.

  • Investigation of Accidents The Occupational Health and Safety Committees, as provided in Clause 22.2, shall be notified of each accident or injury and shall investigate and report to the Union and Employer on the nature and cause of the accident or injury. In the event of a fatality the Employer shall immediately notify the President of the nature and circumstances of the accident.

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