An epistemic interpretation of paraconsistent weak kleene logic damian e. We give a direct application of paraconsistency and address the challenge of developing paraconsistent models with immediate. Dynamic epistemic logic stanford encyclopedia of philosophy. The paper defines a paraconsistent and paracomplete. Remarks on the epistemic interpretation of paraconsistent logic. Paraconsistent logic internet encyclopedia of philosophy. The logic ciore enjoys extreme features concerning propagation and retropropagation of the consistency operator. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. Remarks on the epistemic interpretation of paraconsistency logic. Tableau systems for some paraconsistent modal logics. Thus, if a consequence relation is paraconsistent, then even in circumstances where the available information is inconsistent, the consequence relation does not explode into triviality.
Handbook of epistemic logic download ebook pdf, epub, tuebl. Paraconsistent logic was born in the vicinity of modal logic. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like graham priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. They also considered a firstorder version of ciore called lfi2. In a recent work, walter carnielli and abilio rodrigues present an epistemically motivated interpretation of paraconsistent logic. Paraconsistent weak kleene logic pwk is the 3valued propositional logic defined on the weak kleene tables and with two designated values. Just like it is consistent in classical modal logic that a formula is true and. The argument ex contradictione quodlibet ecq is paraconsistently invalid. A logic is paraconsistent iff its logical consequence relation \\vdash\, either semantic or proof theoretic is not explosive. An epistemic interpretation of paraconsistent weak kleene logic. One axiom, or principle, common to all systems of classical logic is the law of noncontradiction, a principle as you know first formulated by the founder of logic, aristotle himself, at the dawn of the subject. Oct 24, 2019 paraconsistent weak kleene logic pwk is the 3valued propositional logic defined on the weak kleene tables and with two designated values. Someone reasoning with a paraconsistent logic can begin with inconsistent premisessay, a moral dilemma, a kantian. Dec 08, 2015 an explication of the difference between epistemic logic, doxastic logic, and justification logic, the logics of knowledge, belief and justification respectively minus the reverb in the original.
Keywords public announcement logic topological semantics homotopy paraconsistent logic 9. In a quest for paraconsistent logics that are maximally paraconsistent. My work on epistemic logic developed from my research in artificial intelligence. A should be accepted without thereby accepting any proposition b whatsoever. This site is like a library, use search box in the widget to get ebook that you want. Pdf the purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which. In their view, when there is conflicting evidence with regard to a proposition a i. Click download or read online button to get handbook of epistemic logic book now. Such a logic is in a certain sense a minimal paraconsistent logic. The use of quali ers such as certainly immediately suggests the use of modal logic, just as luk asiewicz \truth value possible does. The expression was coined by the peruvian philosopher mir o quesada as an answer to newton da costa looking for a good name for the systems he was working on. This paper extends fittings epistemic interpretation of some kleene logics to also account for paraconsistent weak kleene logic.
Del pronounced dell is a highly active area of applied logic that touches on topics in many areas, including formal and social epistemology, epistemic and doxastic logic, belief revision, multiagent and distributed systems, artificial intelligence, defeasible and nonmonotonic reasoning, and epistemic game theory. The adequacy of a logic to a particular context, or domain, depends on three factors. Agm theory of belief revision to paraconsistent logics will be mentioned. Sowa this is a preprint of chapter 23 in epistemic logic. One can be a paraconsistent logician without being a dialetheist, since paraconsistent logics may be studied and developed without the commitment to the truth of. On formal aspects of the epistemic approach to paraconsistency. Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge.
To achieve this goal, a dualization of fittings cutdown operator is discussed, leading to the definition of a trackdown operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. The paper defines a paraconsistent and paracomplete natural deduction system, called the basic logic of evidence ble, and extends it to the logic of evidence and truth letj. To me, from the family of paraconsistent and paracomplete logics, relevant logic is one of the logics offering most sufficiently the notion of consequence, both in semantic and syntactic plan. While epistemology has a long philosophical tradition dating back to ancient greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics. Holliday university of california, berkeley abstract this chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. Modal logic epistemic logic artificial intelligence. Szmuc abstract this paper extends fittings epistemic interpretation of some kleene logics, to also account for paraconsistent weak kleene logic. Handbook of epistemic logic download ebook pdf, epub.
Initially, d2 was presented as a modal logic in disguise. On the other hand, the existence of such binary opera. An epistemic interpretation of paraconsistent weak kleene. To achieve this goal, a dualization of fittings \cutdown. The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. We study several paraconsistent threevalued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers to the literature.
The second goal of the article is to adapt to qciore the partial structures semantics for the firstorder paraconsistent logic lpt1 introduced by coniglio and silvestrini, which generalizes the semantic notion of quasitruth considered by mikeberg, da costa and chuaqui. This fact motivates epistemic logics based on paraconsistent logic, examples of which can be traced back at least to the 1980s. Remarks on the epistemic interpretation of paraconsistency. We provide a cutfree calculus a hybrid between a natural deduction calculus and a. A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Nov 23, 2017 the purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Logical studies of paraconsistent reasoning in science and. Paraconsistent logic is a eld of research based on the distinction between contradiction and triviality. Modal logic epistemic logic eric pacuit university of maryland, college park ai. From paraconsistent threevalued logics to multiplesource epistemic logic article pdf available august 20 with 26 reads how we measure reads.
Two formal systems are surveyed, the basic logic of evidence ble and the logic of evidence and truth letj, designed to deal, respectively, with evidence and with evidence and truth. Remarks on the epistemic interpretation of paraconsistent. Handbook of the 5th world congress on paraconsistency. These logics handle inconsistent and nontrivial information, but they usually do not. Modelling sources of inconsistent information in paraconsistent. Crucially, for our logic to be inconsistencytolerant but nontrivial, it. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Pdf from paraconsistent threevalued logics to multiple. Chapter 9 public announcements and inconsistencies. Epistemic logics based on normal modal logic are notoriously bad at handling inconsistent and yet nontrivial information. Most of the existing proof systems for pwk are characterised by the presence of linguistic restrictions on some of their rules.
Someone reasoning with a paraconsistent logic can begin with. Several interpretations can be given to the third truth value in threevalued logics. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition a is understood as reasons for believing that a is true. No previous exposure to epistemic logic is assumed.
They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, manyvalued logic, relevance and paraconsistent logic, free logics, extensional v. In this approach, the state of a distributed system is characterized using epistemic concepts, such as, the information available to each processor what the processor knows. Epistemic interpretation of paraconsistent logic 155 not accepting a pair of contradictory propositions but suspending judgment. Obviously, by itself, tweak ing the formal apparatus of epistemic logic does not solve traditional epistemological problems. The future of paraconsistent logic will depend on a right analysis of the various di. Relations between paraconsistent logic and other logics. Paraconsistent logic stanford encyclopedia of philosophy. Clearly, unknown means that true and false are possible5. Dynamic epistemic logic is the study of modal logics of model change. Finally, some important results of classical model theory are obtained for.
The two goals of the current work are closely connected both logically and game theoretically. Considered a kind of dynamic epistemic logic, public announcement logic works as follows. Threevalued logics for incomplete information and epistemic logic 3 singleton. Published version in journal of philosophical logic,vol. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent or inconsistencytolerant systems of logic. Moreover, as every other nonclassical logicians, paraconsistentists have very often.
People saying that there are contradictions everywhere, without any rational support, and that paraconsistent logic is therefore our salvation, are similar to people alerting about a terrible. Contradictions are, instead, epistemically understood as con. A logic with the property that any formula can be deduced from every set of hypotheses that contains contradictory formulas but one is far from a reasonable paraconsistent logic. An explication of the difference between epistemic logic, doxastic logic, and justification logic, the logics of knowledge, belief and justification respectively minus the reverb in the original. In a non paraconsistent logic, inconsistency explodes in the sense that if a contradiction obtains, then everything everything. The chapter also discusses the relation between paracomplete and paraconsistent logics and analyzes some key notions related to paraconsistency, such as. From paraconsistent threevalued logics to multiplesource.
710 1163 1163 677 998 604 411 368 1132 979 632 173 446 454 1041 1033 689 831 1050 1296 186 967 634 799 835 385 337 603 311 484 1193 189 242 1150 1443 2 1072 859 763 643 51 472 658 544 1446