
563 S.E.2d 739 (2002)
264 Va. 89
AMCHEM PRODUCTS, INC., et al.,
v.
NEWPORT NEWS CIRCUIT COURT ASBESTOS CASES, Plaintiffs.
Record No. 012576.
Supreme Court of Virginia.
June 7, 2002.
*740 Richard M. Wyner (John Moustakas; Richard L. Matheny, III; Bruce T. Bishop; Joyce Jackson Wood; Stephen R. Jackson; Daniel T. Campbell; Shea & Gardner; Wilcox & Savage, on briefs), Norfolk, for appellants.
Donald Patten (Avery T. Waterman, Jr., Newport News; Richard S. Glasser, Norfolk; Patten, Wornom, Hatten, & Diamonstein, Newport News; Glasser & Glasser, Norfolk, on brief), for appellees.
Present: All the Justices.
HASSELL, Justice.
In this interlocutory appeal, we consider whether the circuit court erred by refusing to require the litigants to resolve their purported dispute in accordance with an arbitration provision in a contract.

II.
Five hundred and ninety-seven individual plaintiffs filed lawsuits in the circuit court against certain asbestos manufacturers and/or distributors, including the defendants, Amchem Products, Inc., C.E. Thurston and Sons, Inc., and Dana Corporation. The plaintiffs, who included personal representatives of the estates of certain decedents, alleged that they, or their decedents, sustained personal injury or that their decedents died as a result of exposure to asbestos.
The defendants are members of the Center for Claims Resolution, a Delaware corporation composed of companies formerly engaged in the manufacture, sale, and/or distribution of asbestos and products that contain asbestos. The Center for Claims Resolution was created for the express purpose of evaluating, negotiating, litigating, and settling asbestos-related personal injury and property damage claims against its members. In July 2000, the Center for Claims Resolution and its members entered into a Master Settlement Agreement with the plaintiffs in this appeal.
Pursuant to the terms of the Master Settlement Agreement, the members of the Center for Claims Resolution agreed to settle each plaintiff's claims against its members for sums specified in the Master Settlement Agreement. The Master Settlement Agreement states in part that "[t]his Settlement Agreement is made by and between the members of the Center for Claims Resolution, specifically, Amchem Products, Inc., Armstrong World Industries, Inc., The Asbestos Claims Management Corporation (formerly known as National Gypsum Company);. . . C.E. Thurston & Sons, Inc.; Dana Corporation;" and certain law firms.
*741 The Master Settlement Agreement, dated July 2000, contained the following provision in paragraph 5(b):
"To encourage the resolution of disputes without the need for arbitration, counsel for the parties shall meet face to face at least twice per year, and seven days prior to each meeting, the parties shall exchange a list of the disputed issues and/or individual cases and the pertinent information regarding those cases or issues. If counsel are unable to resolve any dispute arising under this agreement, including either its interpretation or application, the matter shall be referred to the McCammon Mediation Group, which shall appoint an independent arbitrator to resolve the matter. In each case, the decision of the arbitrator shall be final and binding upon the parties, and the cost of arbitration, including the arbitrator's fees and expenses, shall be borne equally by the parties, and each party shall bear its own attorneys' fees."
On October 16, 2000, Michael Rooney, chief claims officer for the Center for Claims Resolution, forwarded a letter to counsel for the plaintiffs. This letter modified the Master Settlement Agreement and stated in relevant part:
"Pursuant to the Master Settlement Agreement between the Center for Claims Resolution and the law firms of Patten, Wornom, Hatten & Diamonstein, L.C., and Glasser & Glasser, P.L.C., for the resolution of qualified cases ... the [Center for Claims Resolution] understands and consents that plaintiffs counsel intends to make payment to all of these qualified plaintiffs in three equal installments rather than in full to three separate groups ... . Specifically, the [Center for Claims Resolution] understands that plaintiff counsel intends to pay each qualified plaintiff the settlement values set forth in Paragraph 2 of the agreement in three equal installments the first of which is due on or about October 30, 2000, the second is due on or about April 30, 2001, and the third is due on or about October 30, 2001.
"Each settling plaintiff will execute a release to the [Center for Claims Resolution] for the full amount of the settlement prior to receiving the first installment; however, it is specifically understood and agreed that these releases are not evidence of full satisfaction of the contractual obligation of the [Center for Claims Resolution] to pay the qualified plaintiffs the settlement values that have been agreed upon, and should the [Center for Claims Resolution] fail to timely make any or all of the payments required by the Master Settlement Agreement, then in that event each settling plaintiff who has not received full payment may pursue a remedy in contract against the [Center for Claims Resolution] members for any deficiency. If such action is required, the [Center for Claims Resolution] members shall be responsible to pay the deficiency with interest at 8% per annum, and the [Center for Claims Resolution] members will reimburse each such settling plaintiff for reasonable attorneys' fees and expenses that may be required to collect this deficiency by lawsuit or otherwise.
"This remedy in contract on the release will be the sole legal remedy of each plaintiff who has executed a release for the full consideration of his settlement but fails to receive timely payment in full."
The plaintiffs' claims were accepted by the Center for Claims Resolution under the Master Settlement Agreement as modified, and each plaintiff executed a release absolving all the Center for Claims Resolution members from any liability.
Prior to the date that the Center for Claims Resolution was required to make the payments specified in the Master Settlement Agreement, two of its members defaulted on their obligations to pay their prescribed share of the payments. The Asbestos Claims Management Corporation declared itself insolvent and failed to pay its obligations. Armstrong World Industries, Inc., filed a petition in bankruptcy and also defaulted on its settlement obligations. In January 2001, the Center for Claims Resolution forwarded a check to plaintiffs' counsel that represented the amounts due from the Center for Claims Resolution member companies other than the Asbestos Claims Management Corporation and Armstrong World Industries, Inc.
*742 Subsequently, the plaintiffs filed a "Motion To Enforce Settlement Agreement" in the circuit court. The plaintiffs asserted that the Center for Claims Resolution and its member companies are individually, jointly, and severally liable to the plaintiffs for the payments due under the Master Settlement Agreement, and interest and attorneys' fees permitted by the agreement, including the October 16, 2000 modification. The defendants, relying upon paragraph 5(b) of the Master Settlement Agreement, asserted that a dispute existed and, therefore, the plaintiffs were required to submit their claims to binding arbitration as required by the Federal Arbitration Act and the Virginia Arbitration Act. The circuit court denied the defendants' motion to compel arbitration, and the defendants filed an interlocutory appeal from that order.

III.

A.
The defendants argue that the circuit court erred in denying their motion to compel resolution of this purported dispute by arbitration. The defendants assert that the Master Settlement Agreement is governed by the Federal Arbitration Act, and the Act reflects a liberal federal policy that favors enforcement of arbitration agreements. The defendants state that paragraph 5(b) of the Master Settlement Agreement contains a mandatory arbitration provision and that the October 16, 2000 letter does not alter the arbitration requirement.
Continuing, the defendants assert that a dispute exists that is subject to binding arbitration because
"the proper interpretation of the October Letter, and the proper application of the [Master Settlement Agreement] in light of the October Letter, is disputed by the parties. The plaintiffs read the letter to create a new contract remedy against `all the [Center for Claims Resolution] members.' The defendants read the letter to confirm the plaintiffs' contract remedy against the `defaulting [Center for Claims Resolution] members.' As such, the plaintiffs' motion to enforce the settlement against the defendants herein necessarily depends in the first instance on an interpretation of the October Letter, and  under the arbitration clause in § 5(b) of the agreement  only an arbitrator has jurisdiction to render such an interpretation."
Responding, the plaintiffs initially contend that this Court lacks jurisdiction of the circuit court's order denying the defendants' motion to compel arbitration because such order cannot be challenged by an interlocutory appeal but must be contested solely by a writ of mandamus. Alternatively, the plaintiffs assert that the October 2000 letter modified the Master Settlement Agreement, by providing the plaintiffs with a new remedy against all members of the Center for Claims Resolution for any deficiencies in payment as provided by the Master Settlement Agreement.
Continuing, the plaintiffs state that the language in the October 2000 letter is clear, unambiguous, and not subject to varying interpretations. Thus, the plaintiffs assert that there is no dispute that the October 2000 letter, which modified the Master Settlement Agreement, gave them a contractual right to pursue an action for breach of contract and reasonable attorneys' fees and expenses against all the Center for Claims Resolution members jointly and severally if the Center for Claims Resolution fails to make the payments required by the Master Settlement Agreement.

B.
Initially, we observe that this Court has jurisdiction to decide whether the plaintiffs' claims are subject to the arbitration agreement. Code § 8.01-581.01 states in part that "[a] written agreement to submit any existing controversy to arbitration or a provision in a written contract to submit to arbitration any controversy thereafter arising between the parties is valid, enforceable and irrevocable, except upon such grounds as exist at law or in equity for the revocation of any contract." Code § 8.01-581.02 confers upon a circuit court the power to compel or stay arbitration proceedings. Code § 8.01-581.016 confers upon this Court jurisdiction *743 to review a circuit court's order that denies or compels arbitration.

C.
Our resolution of this appeal is governed in part by the Federal Arbitration Act because the Master Settlement Agreement, as modified by the October 2000 letter, "involved interstate commerce." Thus, we must apply the federal substantive law to determine whether the parties must submit to binding arbitration as required by the contract. Allied-Bruce Terminix Cos. v. Dobson, 513 U.S. 265, 268-70, 281-82, 115 S.Ct. 834, 130 L.Ed.2d 753 (1995); see 9 U.S.C. § 1, et seq. (2000). Therefore, we must apply the following federal principles.
The question whether a party has agreed to arbitrate a particular issue is a matter of contract interpretation. The Supreme Court has stated that a "party cannot be required to submit to arbitration any dispute which he has not agreed so to submit." United Steelworkers of America v. Warrior & Gulf Navigation Co., 363 U.S. 574, 582, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960). The Federal Arbitration Act contains "a congressional declaration of a liberal federal policy favoring arbitration agreements, notwithstanding any state substantive or procedural policies to the contrary. The effect of [§ 2 of the Act] is to create a body of federal substantive law of arbitrability, applicable to any arbitration agreement within the coverage of the Act." Moses H. Cone Memorial Hospital v. Mercury Constr. Corp., 460 U.S. 1, 24, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983).
The Supreme Court has stated that the Federal Arbitration Act "establishes that, as a matter of federal law, any doubts concerning the scope of arbitrable issues should be resolved in favor of arbitration, whether the problem at hand is the construction of the contract language itself or an allegation of waiver, delay, or a like defense to arbitrability." Id. at 24-25, 103 S.Ct. 927 (footnote omitted). This strong presumption of arbitrability mandates that a court must require the parties to submit to arbitration if the scope of an arbitration clause subject to the federal act is open to question. American Recovery Corp. v. Computerized Thermal Imaging, Inc., 96 F.3d 88, 92 (4th Cir.1996); Peoples Sec. Life Ins. Co. v. Monumental Life Ins. Co., 867 F.2d 809, 812 (4th Cir. 1989).
The Supreme Court has held that a court must compel parties to arbitrate pursuant to the terms of an agreement covered by the federal Act "unless it may be said with positive assurance that the arbitration clause is not susceptible of an interpretation that covers the asserted dispute." Warrior & Gulf Navigation Co., 363 U.S. at 582-83, 80 S.Ct. 1347; accord Long v. Silver, 248 F.3d 309, 316 (4th Cir.), cert. denied, ___ U.S. ___, 122 S.Ct. 213, 151 L.Ed.2d 151 (2001).
However, in determining whether a contractual dispute exists that is subject to arbitration, we must review the language contained in the Master Settlement Agreement and the October 2000 modification to ascertain the meaning of these documents, and in making this determination, we must apply the substantive contract law of this Commonwealth. The question "[w]hether a party agreed to arbitrate a particular dispute is an issue for judicial determination to be decided as a matter of contract." Johnson v. Circuit City Stores, Inc., 148 F.3d 373, 377 (4th Cir.1998); accord AT & T Technologies, Inc. v. Communications Workers of America, 475 U.S. 643, 648-49, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986); Arrants v. Buck, 130 F.3d 636, 640 (4th Cir,1997). In making this determination, the courts should apply "ordinary state-law principles that govern the formation of contracts." First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 944, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995); see also Arrants, 130 F.3d at 640 ("[c]ourts decide whether there is an agreement to arbitrate according to common law principles of contract law").

D.
The litigants agree that the letter that the Center for Claims Resolution's Chief Claims Officer, Rooney, forwarded to the plaintiffs' counsel changed the terms of the Master Settlement Agreement. It is well established that a written contract can be modified by an express mutual agreement, *744 which may be in writing. Stanley's Cafeteria v. Abramson, 226 Va. 68, 72, 306 S.E.2d 870, 872 (1983).
We have stated that "[c]ontracts between parties are subject to basic rules of interpretation. Contracts are construed as written, without adding terms that were not included by the parties." TM Delmarva Power v. NCP of Virginia, 263 Va. 116, 119, 557 S.E.2d 199, 200 (2002); accord Wilson v. Holyfield, 227 Va. 184, 187, 313 S.E.2d 396, 398 (1984). Additionally, it is well established that when the terms of a contract are clear and unambiguous, a court must give them their plain meaning. Pocahontas Mining Co. v. Jewell Ridge Coal Corp., 263 Va. 169, 173, 556 S.E.2d 769, 771 (2002); Golding v. Floyd, 261 Va. 190, 192, 539 S.E.2d 735, 736 (2001); Bridgestone/Firestone v. Prince William Square, 250 Va. 402, 407, 463 S.E.2d 661, 664 (1995); Foods First, Inc. v. Gables Associates, 244 Va. 180, 182, 418 S.E.2d 888, 889 (1992). We must construe the words as written in the contract, and we will not make a new contract for the parties. Bridgestone, 250 Va. at 407, 463 S.E.2d at 664; Berry v. Klinger, 225 Va. 201, 208, 300 S.E.2d 792, 796 (1983).
Applying these contract principles, we are compelled to conclude, with positive assurance, that the plaintiffs' claims are not subject to the arbitration provision in the Master Settlement Agreement because a legally cognizable dispute does not exist. There is no dispute about the terms of the October 16, 2000 letter that modified the Master Settlement Agreement. There is no dispute that the language contained in the second paragraph of the October 2000 letter confers upon the plaintiffs the right to "pursue a remedy in contract against the [Center for Claims Resolution] members" for any deficiency in the event the Center for Claims Resolution fails to timely make any payments required by the Master Settlement Agreement. There is no dispute that the Center for Claims Resolution failed to pay the plaintiffs as required by the terms of the Master Settlement Agreement. Additionally, the October 2000 letter explicitly states that this "remedy in contract on the release will be the sole legal remedy of each plaintiff who has executed a release for the full consideration of his settlement but fails to receive timely payment in full."
The defendants, however, assert that the plaintiffs' contractual remedies are limited to claims against the defaulting members of the Center for Claims Resolution and not "all the members of the Center for Claims Resolution?' Thus, the defendants say that this difference in interpretation creates a dispute subject to resolution by an arbitrator pursuant to the terms of the arbitration provision in the Master Settlement Agreement.
Contrary to the defendants' assertions, there can be no legally cognizable dispute regarding the meaning of the clear and unambiguous language contained in the October 2000 letter. As we have already stated, we must apply the plain meaning of the contract language in ascertaining the parties' rights, and pursuant to the plain meaning of the language used in the October 2000 modification, the plaintiffs have the right to "pursue a remedy in contract against the [Center for Claims Resolution] members for any deficiency." This clear and unambiguous language does not limit the plaintiffs' contract remedies to the defaulting Center for Claims Resolution members. We will not add words to the litigants' contract. Rather, we must enforce the contract using the express words that the Center for Claims Resolution chose to employ when making the written modification to the Master Settlement Agreement. As we have held:
"It is the function of the court to construe the contract made by the parties, not to make a contract for them. The question for the court is what did the parties agree to as evidenced by their contract. The guiding light in the construction of a contract is the intention of the parties as expressed by them in the words they have used, and courts are bound to say that the parties intended what the written instrument plainly declares."
Graphic Arts Mutual Ins. v. C.W. Warthen Co., 240 Va. 457, 460, 397 S.E.2d 876, 878 (1990) (quoting Magann Corp. v. Electrical Works, 203 Va. 259, 264, 123 S.E.2d 377, 381 (1962)). Moreover, a dispute that subjects a *745 party to arbitration must be real and not A contrary conclusion would permit a litigant to assert the existence of a purported dispute when there is no basis in fact or law to do so, thereby depriving the opposing litigant of valuable contractual rights.
Thus, reiterating, we hold that the circuit court did not err in denying the defendants' request to arbitrate because, applying the federal law and the Federal Arbitration Act, we conclude with positive assurance that no legally cognizable dispute exists that would subject the litigants to arbitration and, thus, there is nothing for an arbitrator to decide,

IV.
We will affirm the interlocutory order appealed from, and we will remand this case to the circuit court so that the plaintiffs may pursue their contract remedies.
Affirmed and remanded.
