# Browsing by Subject "Logic"

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Item Argumengine: A Computer Augmented Approach to Argument Analysis(2021-05) Davis, T. AlexanderShow more Arguments are indispensable to reasoning. At their most precise, they are proofs, and form the foundation of mathematics. Still, at lower levels of precision, they are pragmatically useful in everyday life. We argue with ourselves and each other to figure out what we ought to do and believe. Over the eons, we have developed tools for interpreting and modeling arguments. Writing, logic, and math are examples. With the advent of computers, the prospect of using programs to represent arguments became evident. Argumengine is a new addition to this class of programs, aiming to improve upon existing systems. First, I review the reasons why computerized argumentation systems are useful, and explain how these reasons informed Argumengine. Then, the argument representation structure used by Argumengine will be described, and its suitability for representing arguments will be explored. Next, the core functions of the software will be described and justified. Finally, some examples will be reviewed to demonstrate the system's use.Show more Item Epistemicism(2015-05) Hu, Ivan J.; Sainsbury, R. M. (Richard Mark); Kamp, Hans; Bonevac, Daniel A.; Koons, Robert C.; Dever, Joshua; Raffman, DianaShow more I propose a new theory of vagueness centered around the epistemology and normativity of vagueness. The theory is a version of epistemicism—the view that vagueness is a fundamentally epistemic phenomenon—that improves upon existing epistemicist accounts by accommodating both the alleged tolerance and open texture of vague predicates, while foregoing excessive metaphysical commitments. I offer a novel solution to the infamous Sorites paradox, one that outrivals alternative contextualist theories in their ability to explain the phenomenology of vagueness as well as its deontic consequences.Show more Item In what sense (if any) is meaning normative?(2018-04-26) Miller, Taylor-Grey; Buchanan, L. Ray (Lawrence Ray)Show more "Meaning is normative" has become a popular dictum in the philosophy of language. Moreover, some proponents of the dictum have appealed to the normativity of meaning in order to demonstrate the hopelessness of a reduction of semantic to non-semantic vocabulary. The upshot, some maintain is that this stands in the way of a naturalistically respectable theory of meaning. The aim of this paper is to get clear on what exactly the dictum should amount to in order to pose a problem for a naturalistic theory of meaning and then see whether the dictum is true. I will argue that the most plausible version of the thesis that meaning is normative poses no real threat to the possibility of naturalism about meaningShow more Item A method to establish non-informative prior probabilities for risk-based decision analysis(2008-08) Min, Namhong; Gilbert, Robert B. (Robert Bruce), 1965-; Lake, Larry W.Show more In Bayesian decision analysis, uncertainty and risk are accounted for with probabilities for the possible states, or states of nature, that affect the outcome of a decision. Application of Bayes’ theorem requires non-informative prior probabilities, which represent the probabilities of states of nature for a decision maker under complete ignorance. These prior probabilities are then subsequently updated with any and all available information in assessing probabilities for making decisions. The conventional approach for the non-informative probability distribution is based on Bernoulli’s principle of insufficient reason. This principle assigns a uniform distribution to uncertain states when a decision maker has no information about the states of nature. The principle of insufficient reason has three difficulties: it may inadvertently provide a biased starting point for decision making, it does not provide a consistent set of probabilities, and it violates reasonable axioms of decision theory. The first objective of this study is to propose and describe a new method to establish non-informative prior probabilities for decision making under uncertainty. The proposed decision-based method is focuses on decision outcomes that include preference in decision alternatives and decision consequences. The second objective is to evaluate the logic and rationality basis of the proposed decision-based method. The decision-based method overcomes the three weaknesses associated with the principle of insufficient reason, and provides an unbiased starting point for decision making. It also produces consistent non-informative probabilities. Finally, the decision-based method satisfies axioms of decision theory that characterize the case of no information (or complete ignorance). The third and final objective is to demonstrate the application of the decision-based method to practical decision making problems in engineering. Four major practical implications are illustrated and discussed with these examples. First, the method is practical because it is feasible in decisions with a large number of decision alternatives and states of nature and it is applicable to both continuous and discrete random variables of finite and infinite ranges. Second, the method provides an objective way to establish non-informative prior probabilities that capture a highly nonlinear relationship between states of nature. Third, we can include any available information through Bayes’ theorem by updating the non-informative probabilities without the need to assume more than is actually contained in the information. Lastly, two different decision making problems with the same states of nature may have different non-informative probabilities.Show more Item Topics in the logic of relevance : towards a theory of entailment(1979) Diaz, Manuel Richard; Martin, Norman M.Show more I investigate the claim of those who believe that considerations of relevance are essential to an analysis of entailment. A hallmark of this claim is that A&-A does not entail any random B, and hence there must be an error in Lewis' proof that it does. Their attack on the "Official View" of entailment has generally suffered from their neglect to give a formal analysis of relevance. Without such an analysis, the arguments of the proponents of relevance cannot compete with the well established classical and intuitionistic theories of deduction. One exception may be the work in relevance logic begun by Anderson and Belnap. Thus I devote a section to their system R and its important neighbors. A systematic and critical appraisal of the system shows that without an independent account of relevance the choice of axioms for the system must be ad hoc. This is so despite the development of formal semantics, and a primitive move towards a theory of relevance embodied in Belnap's claim that "a necessary condition for A's being relevant to B is that they share a propositional variable." Hence it is essential to give a formal characterization of relevance before we may ascertain the part it plays in the analysis of entailment. I give two formal criteria of relevance, truth functional relevance and occurrence relevance, and investigate their formal properties The investigation of systems which embody these formal relevance criteria enables me to develop a theory of the part relevance plays in logical study. My position is that relevance logic is not, and should not be, the primary tool for logical studies. In most cases we are primarily interested in the kind of logical connection exemplified by the classical concept of deducibility. However, there are logical inquiries in which relevance logic plays a crucial role, and our intuitions in these areas appear to be compatible with the formal relevance logics that I develop. For when we study the strength of assumptions, alternative foundations, or the structure of proofs or systems, we are very much concerned with relevance. In particular, relevance appears to be involved with the concept of mathematical elegance. Thus, relevance is perhaps not essential to deduction, but is a valid area of concern for the logicianShow more