Propertarianism is a political philosophy, generally traced back to Locke and the Levellers, whose basic tenets have been systematically supported in the writings of Murray Rothbard, Hans-Hermann Hoppe, and others. Propertarian analysis produces such statements as “Justice is served when no non-consensual appropriations of property rights or titles occurs,” “One owns one's own body,” and "Retribution and restitution for non-consensual appropriations of property rights (torts) should be proportional."
The most significant attempt to apply propertarianism to the problem of the morality of abortion was Walter Block's Evictionism. Block boiled the problem down to the two propositions below:
1. Life begins at conception, and a fetus is fully-endowed with the rights of self-ownership, including the right not to have one's life non-consensually terminated.
2. A woman is an absolute self-owner and doesn't have to allow her body to be used for pregnancy against her will.
Block argues that in spite of #1 above, the fetus is a trespasser on the woman's property and that abortion of an unwanted fetus would be act of self-defense. According to propertarian theory, violent coercion is permissible in defense of self or property or in legal proceedings based on just legal principles. However, if abortion entails the killing of the fetus, that's a problem for Block (because of #1). Although a woman may evict a fetus from her womb, the doctor performing the abortion is obligated to try to save the fetus' life if technologically feasible.
Wisniewski opined the harm of evicting the fetus from the mother's womb is disproportionately greater that the harm done in requiring the non-consenting mother to carry the fetus to full term (or at least to the point where it can be removed without killing it). So Evictionism is charged with violating the rule of proportionality.
Justice theory (i.e. political philosophy) is built on the premise that the individuals subject to its analysis are discrete human beings. A woman and her fetus do not fit the criterion of being discrete human beings. Therefore, I conclude that, when it comes to the morality of abortion, political philosophy is the wrong tool for the job. The moral rules that apply to the morality of abortion could be the rules that govern one's personal behavior, but not the rules that concern interaction.
Although Evictionism went very far in the application of propertarianism to the moral problem of abortion, it could not overcome the basic unsuitability of any kind of political philosophy for the task.
References
Wisniewski, “Rejoinder to Block's Defense of Evictionism,” Libertarian Papers, Vol. 2, No. 37 (2010).