A Paraconsistent Higher Order Logic

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker, Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte

A Paraconsistent ASP-like Language with Tractable Model Generation

Answer Set Programming (ASP) is nowadays a dominant rule-based knowledge representation tool. Though existing ASP variants enjoy efficient implementations, generating an answer set remains intractable. The goal of this research is to define a new \asp-like rule language, 4SP, with tractable model generation. The language combines ideas of ASP and a paraconsistent rule language 4QL. Though 4SP shares the syntax of \asp and for each program all its answer sets are among 4SP models, the new language differs from ASP in its logical foundations, the intended methodology of its use and complexity of computing models. As we show in the paper, 4QL can be seen as a paraconsistent counterpart of ASP programs stratified with respect to default negation. Although model generation of well-supported models for 4QL programs is tractable, dropping stratification makes both 4QL and ASP intractable. To retain tractability while allowing non-stratified programs, in 4SP we introduce trial expressions interlacing programs with hypotheses as to the truth values of default negations. This allows us to develop a~model generation algorithm with deterministic polynomial time complexity. We also show relationships among 4SP, ASP and 4QL

Generalized belief change with imprecise probabilities and graphical models

We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored

After the Fire the Embers Still Burn: A Theory of Jus Post Bellum

Ending wars right and justly has been an ethical imperative since they have first been fought. Given that the postwar periods of numerous wars fought in the recent past have been seriously bungled, the need for postwar ethics has become perspicuously clear. This need is also striking. It is striking because theories of jus post bellum have recently begun to take shape, yet they remain seriously deficient. Jus post bellum theorizing often remains narrowly focused on interstate warfare and is not reflective of the existing complexity and modalities of twenty first century conflict. In addition, current theories typically focus on punishment, recriminations, and backward–looking models of justice that do not necessarily prioritize relief and aid to war-torn soldiers, societies, and civilians. By theorizing the concept of jus post bellum as a forward-looking cosmopolitan model of justice, where the central task is on building a just and lasting peace through stabilization, aid, and development, this dissertation aims to fill this gap. In so doing, the dissertation seeks to broaden the scope of jus post bellum by connecting it, and the just war tradition more generally, with the emerging contemporary literature of cosmopolitan global justice

Is the Establishment Clause Asymmetrical?

Through numerous Establishment Clause cases, the Supreme Court has concluded that when public educators promote or denigrate religious views in the K-12 classroom, they violate the First Amendment. The Court has found that the protection of ‘freedom of conscience’ is embedded in the purpose of the Establishment Clause, which applies most strictly to the public school setting. This is because the sphere of conscience is most vulnerable to invasion in developing minds, and children are in a captive environment at school - they cannot escape from State instruction. Thus, states, school systems, and teachers who impose their religious beliefs onto students are using State funds to invade the freedom of conscience that the Establishment Clause is designed to protect. The moral egregiousness and unconstitutionality of public educators advancing their religion in the classroom have been absorbed into the public consciousness. The Court has found that the First Amendment, not just the Establishment Clause, is designed to protect the sphere of intellect and conscience, especially of K-12 public school students. However, the constitutional prohibitions on advancing beliefs and opinions in the classroom only cover the category of religion, due to the relevant cases’ Establishment Clause jurisdiction. But even if there are constitutional and perhaps policy differences, there seems to be no meaningful philosophical difference between the reasons why schools and teachers should not advance their religion or ideology in the classroom. When views stemming from either area are imposed on students, we say that someone is being instructed “what to think” rather than “how to think,” constituting an attempt at indoctrination, which the court system recognizes is inimical to the purposes of public education. Through analyzing the Court’s language this paper synthesizes a Court-created conceptual schema that demonstrates the Court’s recognition of the equivalence between advancing religious and ideological views in public school settings. Thus, the Court has created what this paper coins the ‘Problem of Asymmetry:’ “A constitution-based restriction or allowance of certain behavior in a certain area, which the court system does not extend to equivalent behaviors because they are not covered by the operable clause in the Constitution.” In light of this particular asymmetry, this paper examines how the court system creates and recognizes this problem and what implications it has on legislatures and the court system. This paper also examines these implications in light of how the court system has opened up a path to resolve the problem

Judicial Impartiality in a Partisan Era

Judicial legitimacy rests on the perception of judicial impartiality. As a partisan gulf widens among the American public, however, there is a growing skepticism of the judiciary’s neutrality on politically sensitive topics. Hardening partisan identities mean that there is less middle ground on political issues and less cooperation among those with differing political views. As a result, the public increasingly scrutinizes judges and judicial candidates for signs of political agreement, distrusting those perceived to support the opposing political party. Judges themselves are not immune to these political forces. In spite of a strong judicial identity that demands impartiality and judicial conduct rules that require judges to avoid even the appearance of bias, judges have the same unconscious biases and preconceptions as anyone else. Moreover, judges must generally have strong political affiliations to reach the bench at all, regardless of whether they are elected or appointed. Drawing the line between mere political affiliation and an inappropriate appearance of partisan bias can therefore be difficult. This Article analyzes the mechanisms available to safeguard judicial impartiality. Although recusal motions are the most common weapon against partisan bias, this Article argues that recusal motions cannot effectively guard against the appearance of bias arising from a judge’s political views. When recusal rules rely on an undefined “appearance” standard, they are susceptible to an interpretive bias that undermines their purpose. Nonetheless, the Article concludes that the appearance of partisan bias in the judicial branch is not so different from other types of unconscious bias. As a result, ordinary procedural tools—including the right to a jury trial and our system of appellate review—may provide a stronger safeguard against judicial bias than recusal motions

09-03 "Economic Writing on the Pressing Problems of the Day: The Roles of Moral Intuition and Methodological Confusion"

Economists are often called on to help address pressing problems of the day, yet many economists are uncomfortable about disclosing the values that they bring to this work. This essay explores how an inadequate understanding of the role of methodology, as related to ethics and human emotions of concern, underlies this reluctance and compromises the quality of economic advice. The tension between caring about the problems, on the one hand, and writing within the existing culture of the discipline, on the other, are illustrated with examples from U.S. policymaking, behavioral economics, and the economics of climate change and global poverty. Potential steps towards a more responsible, "strongly objective," and policy-useful economics are discussed.