A Plausibility Semantics for Abstract Argumentation Frameworks

We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default reasoning. In this context, we consider the path from structured to logical to shallow semantic instantiations. The resulting well-justified JZ-extension semantics diverges from more traditional approaches.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014). This is an improved and extended version of the author's ECSQARU 2013 pape

External Validity: From Do-Calculus to Transportability Across Populations

The generalizability of empirical findings to new environments, settings or populations, often called "external validity," is essential in most scientific explorations. This paper treats a particular problem of generalizability, called "transportability," defined as a license to transfer causal effects learned in experimental studies to a new population, in which only observational studies can be conducted. We introduce a formal representation called "selection diagrams" for expressing knowledge about differences and commonalities between populations of interest and, using this representation, we reduce questions of transportability to symbolic derivations in the do-calculus. This reduction yields graph-based procedures for deciding, prior to observing any data, whether causal effects in the target population can be inferred from experimental findings in the study population. When the answer is affirmative, the procedures identify what experimental and observational findings need be obtained from the two populations, and how they can be combined to ensure bias-free transport.Comment: Published in at http://dx.doi.org/10.1214/14-STS486 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1312.748

Complete Additivity and Modal Incompleteness

In this paper, we tell a story about incompleteness in modal logic. The story weaves together a paper of van Benthem, `Syntactic aspects of modal incompleteness theorems,' and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, V-BAOs. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem's paper resolves the open question in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to V-BAOs, namely the provability logic GLB. We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is V-complete. After these results, we generalize the Blok Dichotomy to degrees of V-incompleteness. In the end, we return to van Benthem's theme of syntactic aspects of modal incompleteness

On the Mental State of Consciousness of Wrongdoing

Mistake about or ignorance of the law does not exculpate in criminal law, except in limited circumstances. Doctrine and theory cognate to this principle are, by now, well developed and understood. But might an actor\u27s awareness of the illegality or wrongfulness of her conduct inculpate — that is, constitute a form of mens rea that establishes or aggravates liability? Trends in recent adjudication in white collar crime suggest that the answer is yes. This article, part of a symposium issue on Adjudicating the Guilty Mind, takes the first pass at describing the mental state of “consciousness of wrongdoing,” assessing its fit with the conceptual architecture of substantive criminal law, and uncovering the many challenges of proof and adjudication that this concept poses. Three conclusions broadly emerge from this initial, and somewhat truncated, inquiry: first, inculpating an actor for adverting to the legal or normative significance of her conduct is an attractive means of dealing with difficult line-drawing problems presented by many white collar offenses; second, the method can be justified on both retributive and deterrent grounds; and third, the practice requires much more thought and precision at the operational level, lest problems inherent in the structure of criminal adjudication be exacerbated in cases in which liability depends on the idea that an actor “knew what she was doing was wrong

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions

On the Mental State of Consciousness of Wrongdoing

Mistake about or ignorance of the law does not exculpate in criminal law, except in limited circumstances. Doctrine and theory cognate to this principle are, by now, well developed and understood. But might an actor\u27s awareness of the illegality or wrongfulness of her conduct inculpate — that is, constitute a form of mens rea that establishes or aggravates liability? Trends in recent adjudication in white collar crime suggest that the answer is yes. This article, part of a symposium issue on Adjudicating the Guilty Mind, takes the first pass at describing the mental state of “consciousness of wrongdoing,” assessing its fit with the conceptual architecture of substantive criminal law, and uncovering the many challenges of proof and adjudication that this concept poses. Three conclusions broadly emerge from this initial, and somewhat truncated, inquiry: first, inculpating an actor for adverting to the legal or normative significance of her conduct is an attractive means of dealing with difficult line-drawing problems presented by many white collar offenses; second, the method can be justified on both retributive and deterrent grounds; and third, the practice requires much more thought and precision at the operational level, lest problems inherent in the structure of criminal adjudication be exacerbated in cases in which liability depends on the idea that an actor “knew what she was doing was wrong

On adaptive decision rules and decision parameter adaptation for automatic speech recognition

Recent advances in automatic speech recognition are accomplished by designing a plug-in maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and language training corpora. Maximum-likelihood point estimation is by far the most prevailing training method. However, due to the problems of unknown speech distributions, sparse training data, high spectral and temporal variabilities in speech, and possible mismatch between training and testing conditions, a dynamic training strategy is needed. To cope with the changing speakers and speaking conditions in real operational conditions for high-performance speech recognition, such paradigms incorporate a small amount of speaker and environment specific adaptation data into the training process. Bayesian adaptive learning is an optimal way to combine prior knowledge in an existing collection of general models with a new set of condition-specific adaptation data. In this paper, the mathematical framework for Bayesian adaptation of acoustic and language model parameters is first described. Maximum a posteriori point estimation is then developed for hidden Markov models and a number of useful parameters densities commonly used in automatic speech recognition and natural language processing.published_or_final_versio

Geometry from divergence functions and complex structures

Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$ to extract a pre-symplectic form and a metric-like tensor on $M\times M$ from a divergence function. These tensors may be pulled back to $M$, and we compute them in the case of an N-dimensional symplex with respect to the Kullback-Leibler relative entropy, and in the case of (a suitable unfolding space of) the manifold of faithful density operators with respect to the von Neumann-Umegaki relative entropy.Comment: 19 pages, comments are welcome

The Meaning of Probative Value and Prejudice in Federal Rule of Evidence 403: Can Rule 403 Be Used to Resurrect the Common Law of Evidence?

In the common law system of evidence, logically relevant evidence is presumptively admissible. The logical relevance of an item of evidence, however, does not guarantee its admission. The common law has developed a number of rules that exclude logically relevant evidence. In some cases, the common law excludes evidence because of doubts about the credibility or reliability of that type of evidence. For example, the best evidence rule rests primarily on skepticism about the trustworthiness of secondary evidence concerning a document\u27s contents.- When the issue is the content of a document, the common law prefers that the document itself be produced in court, because the production of the document is obviously the most reliable method of establishing its contents. The common law enforces this preference by excluding other evidence of the document\u27s contents, such as oral testimony describing the document, unless there is an adequate excuse for the nonproduction of the document. In other cases, the common law excludes evidence to promote a social policy. The common-law privileges for confidential relationships are illustrative. For example, the attorney-client privilege often bars the admission of relevant, trustworthy evidence in order to encourage the flow of information between client and attorney. The Federal Rules of Evidence became effective on June 1, 1975.The Rules are now in effect not only in federal court, but also in the thirty-one states that have adopted evidence codes patterned after the Federal Rules.6 While the Federal Rules codify most of the common-law exclusionary rules of evidence, the Rules omit others. For example,almost all jurisdictions require that a prosecutor corroborate any confession by the defendant.\u27 In order to introduce a defendant\u27s confession, the prosecutor must present independent, corroborating evidence that a criminal act has occurred. The rationale for the corroboration requirement is doubt about the credibility of confession evidence; confessions are sometimes coerced, and even when there is no police coercion, an innocent person may have an ulterior motive or psychological compulsion to confess to a crime., The corroboration requirement is one of the common-law doctrines omitted from the Federal Rules of Evidence. In other jurisdictions, as a matter of decisional law the courts decided to exclude generally any statements made by a defendant during plea bargaining. These courts did so to further the social policy of encouraging plea bargaining, which eases the burden on the criminal justice system. Under this case law doctrine, if the police questioned the defendant and the defendant reasonably believed that he could bar-gain for concessions during the questioning, the defendant\u27s statement to the police might be excludible. Like the corroboration rule, how-ever, this doctrine has been omitted from the Federal Rules; the only exclusionary rule recognized by the Federal Rules is restricted to plea discussions with an attorney for the prosecuting authority ...

Quasi-Polish Spaces

We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is level \Pi_2 in the Borel hierarchy. Quasi-Polish spaces can be characterized within the framework of Type-2 Theory of Effectivity as precisely the countably based spaces that have an admissible representation with a Polish domain. They can also be characterized domain theoretically as precisely the spaces that are homeomorphic to the subspace of all non-compact elements of an \omega-continuous domain. Every countably based locally compact sober space is quasi-Polish, hence every \omega-continuous domain is quasi-Polish. A metrizable space is quasi-Polish if and only if it is Polish. We show that the Borel hierarchy on an uncountable quasi-Polish space does not collapse, and that the Hausdorff-Kuratowski theorem generalizes to all quasi-Polish spaces