FINE, J.
This is an appeal by the Dog Federation of Wisconsin, Inc., and four persons who claim to own dogs that may be subject to regulation by a City of South Milwaukee ordinance that imposes restrictions on the ownership and keeping of "pit bulls."1 The Fed-[358]*358©ration and the individual appellants claim that the "pit bull" aspects of the ordinance are facially invalid for the following reasons: 1) the definition of "pit bull" is impermissibly vague; 2) the ordinance is overbroad; and 3) the ordinance violates their right to equal protection of the law. We affirm.
The parties filed cross motions for summary judgment in the trial court.2 They thus, in effect, stipulated that there were no issues for trial and that the validity vel non of the ordinance could be decided on the record [359]*359of their submissions. See Grotelueschen v. American Family Ins., 171 Wis. 2d 437, 446-447, 492 N.W.2d 131, 134 (1992). The trial court upheld the ordinance. Our review is de novo. See Green Spring Farms v. Kersten, 136 Wis. 2d 304, 315, 401 N.W.2d 816, 820 (1987).
The focus of the claims by the Federation and the individual appellants is on the ordinance's definition of "pitbull":
"Pit Bull" as used in this ordinance means: Any pit bull terrier, which shall be defined as any American Pit Bull Terrier or Staffordshire Bull Terrier or American Staffordshire Terrier breed of dog, or any mixed breed of dog which contains as an element of its breeding the breed of American Pit Bull Terrier or Staffordshire Bull Terrier or American Stafford-shire Terrier as to be identifiable as partially of the breed of American Pit Bull Terrier or Staffordshire Bull Terrier or American Staffordshire Terrier.
Ordinances, like statutes, are presumed to be constitutional and will be upheld unless shown to be unconstitutional beyond a reasonable doubt. Eastman v. City of Madison, 117 Wis. 2d 106, 111, 342 N.W.2d 764, 767 (Ct. App. 1983). We address the claims of the Federation and the individual appellants in sequence.
1. Vagueness.
A law regulating conduct must give adequate notice of what is prohibited, so as not to delegate "basic policy matters to policemen, judges, and juries for resolution on an ad hoc and subjective basis." Grayned v. City of Rockford, 408 U.S. 104, 108-109 (1972). Thus, "a statute which either forbids or requires the doing of [360]*360an act in terms so vague that men of common intelligence must necessarily guess at its meaning and differ as to its application violates the first essential of due process of law." Connally v. General Constr. Co., 269 U.S. 385, 391 (1926). Although the enactment must have "a reasonable degree of clarity," Roberts v. United States Jaycees, 468 U.S. 609, 629 (1984), exacting precision is not required, Grayned, 408 U.S. at 110, unless the enactment infringes rights that are specifically protected by the constitution, such as those of free speech and association protected by the First Amendment, Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 499 (1982). In short, if a statute or ordinance does not directly affect constitutionally-protected interests, we may not hold it facially-invalid for vagueness even though "doubts as to the applicability of [the challenged] language in marginal fact situations may be conceived." See United States v. Powell, 423 U.S. 87, 93 (1975). With these principles in mind, we turn to the City of South Milwaukee ordinance.
The Federation and the individual appellants contend that an ordinary person would not be able to discern whether a dog is a "pit bull" as defined by the ordinance. They point to the City of South Milwaukee's concession that such a determination would require expert testimony at trial, and that no "current city employee" would be able to give that testimony.
The core of the appellants' factual submissions on their void-for-vagueness argument is an affidavit by Robert M. Brown, D.M.V., the chief veterinarian at the Jackson Area Pet Hospital in Jackson, Wisconsin. Dr. Brown has written various books on dog-ownership, is a columnist for two dog periodicals, and is a dog-show judge certified by the American Kennel Club. Distilled [361]*361judge certified by the American Kennel Club. Distilled to its essential points, the argument advanced by Dr. Brown's affidavit is that:
1) the breed standards referenced by the ordinance are that of the "ideal" dog of that breed;
2) non-experts would be unable to accurately determine whether a particular dog was the "pit bull" defined in the ordinance;
3) experts "would have difficulty determining whether a particular dog was 'identifiable' as being 'partially of one of the breeds named" in the ordinance "solely upon the basis of a visual inspection" (emphasis added);
4) it is "extremely difficult" for him to understand and apply the ordinance's phrase "any mixed breed of dog which contains as an element of its breeding the breed of American Pit Bull Terrier or Staffordshire Bull Terrier or American Staffordshire Terrier" (emphasis added);
5) there is no "genetic method" to determine a dog's breed; and
6) the "only possible way in which a dog might be 'identifiable' as falling within the breeds specified in the South Milwaukee Ordinance is by examining a breeding history that is presented by the dog's owner as part of registering the dog as a purebred animal," and that "the vast majority of dogs" are not registered and lack sufficient breeding documentation, so that the only way oí "truly determining the breed of dog" would be to breed the dog for several generations and examine the offspring. (Emphasis added.)
[362]*362The ordinance's definition of "pit bull" makes specific reference to breeds that are recognized by both the American Kennel Club and the United Kennel Club. A "breed" is "a relatively homogenous groups of animals within a species, developed and maintained by man." American Kennel Club, Dogs 5 (1991). According to the record in this case, the American Kennel Club has established standards for the American Staffordshire Terrier and the Staffordshire Bull Terrier, while the United Kennel Club has established standards for the Staffordshire Bull Terrier and the American Pit Bull Terrier. The American Staffordshire Terrier was accepted by the American Kennel Club for registration in 1935.3
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FINE, J.
This is an appeal by the Dog Federation of Wisconsin, Inc., and four persons who claim to own dogs that may be subject to regulation by a City of South Milwaukee ordinance that imposes restrictions on the ownership and keeping of "pit bulls."1 The Fed-[358]*358©ration and the individual appellants claim that the "pit bull" aspects of the ordinance are facially invalid for the following reasons: 1) the definition of "pit bull" is impermissibly vague; 2) the ordinance is overbroad; and 3) the ordinance violates their right to equal protection of the law. We affirm.
The parties filed cross motions for summary judgment in the trial court.2 They thus, in effect, stipulated that there were no issues for trial and that the validity vel non of the ordinance could be decided on the record [359]*359of their submissions. See Grotelueschen v. American Family Ins., 171 Wis. 2d 437, 446-447, 492 N.W.2d 131, 134 (1992). The trial court upheld the ordinance. Our review is de novo. See Green Spring Farms v. Kersten, 136 Wis. 2d 304, 315, 401 N.W.2d 816, 820 (1987).
The focus of the claims by the Federation and the individual appellants is on the ordinance's definition of "pitbull":
"Pit Bull" as used in this ordinance means: Any pit bull terrier, which shall be defined as any American Pit Bull Terrier or Staffordshire Bull Terrier or American Staffordshire Terrier breed of dog, or any mixed breed of dog which contains as an element of its breeding the breed of American Pit Bull Terrier or Staffordshire Bull Terrier or American Stafford-shire Terrier as to be identifiable as partially of the breed of American Pit Bull Terrier or Staffordshire Bull Terrier or American Staffordshire Terrier.
Ordinances, like statutes, are presumed to be constitutional and will be upheld unless shown to be unconstitutional beyond a reasonable doubt. Eastman v. City of Madison, 117 Wis. 2d 106, 111, 342 N.W.2d 764, 767 (Ct. App. 1983). We address the claims of the Federation and the individual appellants in sequence.
1. Vagueness.
A law regulating conduct must give adequate notice of what is prohibited, so as not to delegate "basic policy matters to policemen, judges, and juries for resolution on an ad hoc and subjective basis." Grayned v. City of Rockford, 408 U.S. 104, 108-109 (1972). Thus, "a statute which either forbids or requires the doing of [360]*360an act in terms so vague that men of common intelligence must necessarily guess at its meaning and differ as to its application violates the first essential of due process of law." Connally v. General Constr. Co., 269 U.S. 385, 391 (1926). Although the enactment must have "a reasonable degree of clarity," Roberts v. United States Jaycees, 468 U.S. 609, 629 (1984), exacting precision is not required, Grayned, 408 U.S. at 110, unless the enactment infringes rights that are specifically protected by the constitution, such as those of free speech and association protected by the First Amendment, Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 499 (1982). In short, if a statute or ordinance does not directly affect constitutionally-protected interests, we may not hold it facially-invalid for vagueness even though "doubts as to the applicability of [the challenged] language in marginal fact situations may be conceived." See United States v. Powell, 423 U.S. 87, 93 (1975). With these principles in mind, we turn to the City of South Milwaukee ordinance.
The Federation and the individual appellants contend that an ordinary person would not be able to discern whether a dog is a "pit bull" as defined by the ordinance. They point to the City of South Milwaukee's concession that such a determination would require expert testimony at trial, and that no "current city employee" would be able to give that testimony.
The core of the appellants' factual submissions on their void-for-vagueness argument is an affidavit by Robert M. Brown, D.M.V., the chief veterinarian at the Jackson Area Pet Hospital in Jackson, Wisconsin. Dr. Brown has written various books on dog-ownership, is a columnist for two dog periodicals, and is a dog-show judge certified by the American Kennel Club. Distilled [361]*361judge certified by the American Kennel Club. Distilled to its essential points, the argument advanced by Dr. Brown's affidavit is that:
1) the breed standards referenced by the ordinance are that of the "ideal" dog of that breed;
2) non-experts would be unable to accurately determine whether a particular dog was the "pit bull" defined in the ordinance;
3) experts "would have difficulty determining whether a particular dog was 'identifiable' as being 'partially of one of the breeds named" in the ordinance "solely upon the basis of a visual inspection" (emphasis added);
4) it is "extremely difficult" for him to understand and apply the ordinance's phrase "any mixed breed of dog which contains as an element of its breeding the breed of American Pit Bull Terrier or Staffordshire Bull Terrier or American Staffordshire Terrier" (emphasis added);
5) there is no "genetic method" to determine a dog's breed; and
6) the "only possible way in which a dog might be 'identifiable' as falling within the breeds specified in the South Milwaukee Ordinance is by examining a breeding history that is presented by the dog's owner as part of registering the dog as a purebred animal," and that "the vast majority of dogs" are not registered and lack sufficient breeding documentation, so that the only way oí "truly determining the breed of dog" would be to breed the dog for several generations and examine the offspring. (Emphasis added.)
[362]*362The ordinance's definition of "pit bull" makes specific reference to breeds that are recognized by both the American Kennel Club and the United Kennel Club. A "breed" is "a relatively homogenous groups of animals within a species, developed and maintained by man." American Kennel Club, Dogs 5 (1991). According to the record in this case, the American Kennel Club has established standards for the American Staffordshire Terrier and the Staffordshire Bull Terrier, while the United Kennel Club has established standards for the Staffordshire Bull Terrier and the American Pit Bull Terrier. The American Staffordshire Terrier was accepted by the American Kennel Club for registration in 1935.3 The Staffordshire Bull Terrier was accepted by the American Kennel Club for registration in 1974, and by the United Kennel Club in 1975.4 The record does not reveal when the United Kennel Club accepted the American Pit Bull Terrier for registration. Descriptive standards and photographs for each of the breeds denominated as a "pit bull" by the ordinance are in the record.
Reference to recognized breeds provides sufficient specifics to withstand a vagueness challenge. Thus, in State v. Peters, 534 So.2d 760 (Fla. Dist. Ct. App. 1988), the court upheld an ordinance that defined "pit bull" to mean "any dog which exhibits those distinguishing characteristics" that "substantially conform to the standards" established either by the "American Kennel Club for American Staffordshire Terriers or Stafford-[363]*363shire Bull Terriers" or by the "United Kennel Club for American Pit Bull Terriers." 534 So.2d at 762. Peters held that the ordinance was not made impermissibly vague by the provision that the ordinance applied even though there were "[t]echnical deficiencies" in a dog's "conformance to the standards." 534 So.2d at 766-767. Similarly, Garcia v. Village of Tijeras, 767 P.2d 355 (N.M. Ct. App. 1988), upheld, albeit after trial, an ordinance banning ownership or possession of any dog "of the breed known as American Pit Bull Terrier." 767 P.2d at 356.5
Although there are decisions that have ruled pit-bull ordinances too vague to pass constitutional muster, see American Dog Owners Ass'n v. City of Des Moines, 469 N.W.2d 416, 417-418 (Iowa 1991) (ordinance banning Staffordshire Terrier, American Pit Bull Terrier, American Staffordshire Terrier or dogs of any "other breed or mixed breed... known as pit bulls, pit bull dogs or pit bull terriers"); American Dog Owners Ass'n v. City of Lynn, 533 N.E.2d 642, 646 (Mass. [364]*3641989) (identification by breed name insufficient) (dictum), the Federation and the individual appellants here have not carried their burden of demonstrating beyond a reasonable doubt that the City of South Milwaukee ordinance is impermissibly vague on its face. As Peters notes," 'the dog owner, who harbors the dogs at his residence, is the one subject to the penalties of the law. He should know the kind of dogs he owns.’" 534 So.2d at 768 n.13 (citation omitted). Simply put, a person acquires a dog for certain physical and mental characteristics. The ordinance puts persons who have or acquire dogs on sufficient notice of the type of dog that is prohibited. Accepting as verities for the purpose of this decision Dr. Brown's conclusions that there is no absolute way to determine whether a dog is in fact a pit bull as defined in the ordinance, those conclusions do not overcome the presumption of constitutionality. Problems of ultimate proof do not make the ordinance unduly vague on its face.6 As succinctly phrased by Peters, whether a dog is within the ordinance "is a matter of evidence, not constitutional law." 534 So.2d at 768.
2. Overbreadth and equal protection.
The contention by the Federation and the individual appellants that the City of South Milwaukee ordinance is overbroad is, as they articulate it in their brief, essentially one of equal protection: they argue [365]*365that the ordinance impermissibly treats "all pit bulls as if they are inherently dangerous, and more prone to cause harm than other dogs as a matter of law." The "overbreadth" doctrine, however, has no application outside the First Amendment context. United States v. Salerno, 481 U.S. 739, 745 (1987). Accordingly, we analyze the equal-protection aspects of this case.
Equal protection of the law is guaranteed by the Fourteenth Amendment to the United States Constitution and by Article I, section 1 of the Wisconsin Constitution.7
Although no precise formula has been developed, the [United States Supreme] Court has held that the Fourteenth Amendment permits the States a wide scope of discretion in enacting laws which affect some groups of citizens differently than others. The constitutional safeguard is offended [366]*366only if the classification rests on grounds wholly irrelevant to the achievement of the State's objective.
McGowan v. Maryland, 366 U.S. 420, 425 (1961). The Wisconsin Supreme Court has identified five factors relevant to the equal-protection analysis:
(1) All classification [sic] must be based upon substantial distinctions which make one class really different from another.
(2) The classification adopted must be germane to the purpose of the law.
(3) The classification must not be based upon existing circumstances only.
(4) To whatever class a law may apply, it must apply equally to each member thereof.
(5) That the characteristics of each class should be so far different from those of other classes as to reasonably suggest at least the propriety, having regard to the public good, of substantially different legislation.
State ex rel. Baer v. City of Milwaukee, 33 Wis. 2d 624, 633, 148 N.W.2d 21, 25-26 (1967) (bracketed material, citations, and ellipses omitted). Each of these criteria "must be satisfied to sustain a legislative classification against an equal-protection attack." Funk v. Wollin Silo & Equip., Inc., 148 Wis. 2d 59, 63, 435 N.W.2d 244, 246 (1989).
The Federation and the individual appellants contend that the ordinance's treatment of all pit bulls as dangerous has "no scientific or empirical basis" and that dangerousness is a function of "environment, training, and upbringing." Dr. Brown's affidavit and an [367]*367affidavit submitted by a breeder and trainer of purebred dogs, who also has master's and bachelor's degrees in experimental psychology with an emphasis in animal behavior, support this contention. The Federation and the individual appellants concede, however, that the focus of their equal-protection argument is whether there is a rational basis for the ordinance's special treatment of pit bulls. See Funk, 148 Wis. 2d at 69, 435 N.W.2d at 248 ("[WJhere fundamental rights or suspect classes are not involved, courts employ only a rational basis as standard of review."). A classification only violates equal protection if it "is arbitrary and has no reasonable purpose or reflects no justifiable public policy." Kallas Millwork Corp. v. Square D. Co., 66 Wis. 2d 382, 388, 225 N.W.2d 454, 458 (1975). On the record here, the City of South Milwaukee ordinance does not violate equal protection.
The record in this case reveals that the City of South Milwaukee common council passed the pit-bull ordinance after considering various police reports of incidents involving pit bulls.8 Additionally, the common council considered a number of articles explaining the potential dangers posed by pit bulls and recounting [368]*368serious attacks by pit bulls on children and adults.9 One of the articles, published by the Wisconsin Humane Society, noted that "[t]he most prominent difference between the pit bull terrier and other breeds is its capability of inflicting very serious damage" and that there have been "twenty fatalities in four years" as the result of attacks on people.10 A study reported in the May/June 1985 issue of Community Animal Control, concluded that pit bulls "are dangerous animals," based on the study's finding that "[t]he number of dog bites, serious bites and deaths is unproportionately greater for adult, male pit bulls." Although reasonable persons might differ on the import of this material, it cannot be said that the City of South Milwaukee ordinance "is arbitrary and has no reasonable purpose or reflects no justifiable public policy." See Kallas Millwork Corp., 66 Wis. 2d at 388, 225 N.W.2d at 458. Stated another way, and applying the five criteria set out in Baer, 33 Wis. 2d at 633, 148 N.W.2d at 25-26, based on the evidence of record, the ordinance is founded on "substantial distinctions" between the breeds of dog covered by the ordinance and other breeds of dog; the ordinance is "germane" to the underlying purpose of the ordinance to protect persons and animals from dangerous dogs; the ordinance's distinction between pit bulls and other dogs is not based on [369]*369"existing circumstances only"; the ordinance applies equally to the affected class of persons owning or keeping pit bulls; and there is a sufficient distinction between pit bulls and other breeds of dog to justify their disparate treatment. The Federation and the individual appellants have not established beyond a reasonable doubt that the ordinance denies them equal protection of the law.
By the Court. — Judgment affirmed.