They also considered a firstorder version of ciore called lfi2. This semantics generalizes flaggs 1985 construction of a model of a modal version of churchs thesis and firstorder arithmetic. A complete quantified epistemic logic for reasoning about. Some have concluded that names cannot be treated as rigid designators in epistemic logic, as they are in alethic modal logic.
Quantified modal logic is the system that combines pure quantificational logic with propositional modal logic. My paper quantifying in can be regarded as an attempt to explain away such idioms for epistemic contexts. The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction. Pdf this chapter provides a brief introduction to propositional epistemic. 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. Epistemic logic is a subfield of epistemology concerned with logical approaches to knowledge, belief and related notions. Epistemic logic stanford encyclopedia of philosophy. Quantified epistemic logics for reasoning about knowledge in. Epistemic logic is the shining star of reschers provocative trilogy on realism, knowledge, and our cognitive imitations. The logic ciore enjoys extreme features concerning propagation and retropropagation of the consistency. A quantified epistemic logic for reasoning about multiagent.
Thus, taken literally, epistemic logic represents the logic of knowledge. Epistemic logics are logics that allow one to reason about knowledge in some way. The variety of senses that logos possesses may suggest the difficulties to be encountered in characterizing the nature and scope of logic. During the late 50ies and 60ies a large controversy concerning the very possibility of quantified.
Though any logic with an epistemic interpretation may be called an epistemic logic, the most widespread type of epistemic logics in use at present are modal logics. Expressiveness and completeness results francesco belardinelli laboratoire ibisc, universite devry, france. Pdf a quantified epistemic logic for reasoning about. While propositional logic can only express facts, autoepistemic logic can express knowledge and lack of knowledge about facts the stable model semantics, which is used to give a semantics to logic programming with negation as failure, can be seen as a. The proof for bisimulation invariance in lk, given by van ditmarsch, french andpinchinat7appliestols5 andlkd45. The logical modalities of possibility and necessity that function in this domain are subject to the following principles. An explication of the difference between epistemic logic, doxastic logic, and justification logic, the logics of knowledge, belief and justification respectively minus the. A complete quantified epistemic logic for reasoning about message passing systems conference paper september 2007 with 26 reads how we measure reads. Pdf a general semantics for quantified modal logic. View academics in quantified epistemic logic on academia. In modern philosophy, however, epistemic logic is used as a technical term not only for the logic of knowledge but also for the.
Epistemic logic is a promising tool for analyzing distributed systems. Epistemic logic routledge encyclopedia of philosophy. We show that eqbl can express relevant properties about agents knowledge in multiagent contexts, such as agent a knows as much as agent b. Knowledge and belief are represented via the modal operators k and b, often with a subscript indicating the. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers to the literature.
New york university new york, new york leora morgenstern ibm watson research center hawthorn, new york august 28, 1983 1 introduction it is to the advantage of a thinking creature to be aware of knowledge and thought and to be able to reason about them. The logic aaul takes arrow update logic, a dynamic epistemic logic where the accessibility relations of agents are updated rather than the set of possible worlds, and adds a quantifier over such. In 9 we developed a semantics for quantified relevant logic that uses general frames. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope. Bengson and moffett 2012, fantl 2016, ichikawa and steup 2017. Finally, we exemplify the use of the logic by modelling message passing systems, a typical class of interpreted systems analysed in epistemic logic. Let us now consider quantified modal logic qml in an epistemic perspective. An introduction to the logic of the two notions hintikka. Modal logic epistemic logic artificial intelligence. Quantified interpreted systems may be used to interpret a variety of firstorder modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We analyse a firstorder epistemic language interpreted on this semantics and show soundness and completeness of the quantified modal system qs5 d n, an axiomatisation for these structures. As opposed to i telieve that my neighbour is at home and that i do not believe it, tile sentence i believe that my neighbour was at home and that i did not believe it is inmmne to the charge of inconsistency gochet, 2004.
Abstract epistemic modal predicate logic raises conceptual. We investigate quantified interpreted systems, a semantics for multiagent systems in which agents. We present syntax and semantics of the language formally and show completeness of an axiomatisation. Quantifiers and quantification stanford encyclopedia of.
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. Quantification, in logic, the attachment of signs of quantity to the predicate or subject of a proposition. For example, the statement john is happy might be qualified by saying that john is usually happy, in which case the term usually is functioning as. Knowledge and belief are represented via the modal. Sowa this is a preprint of chapter 23 in epistemic logic. A quantified epistemic logic for reasoning about multiagent systems conference paper pdf available january 2007 with 27 reads how we measure reads. Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by hintikka 1962. Beyond philosophy proper, epistemic logic flourishes in theoretical. This article proposes an account of knowingwho constructions within a generalisation of hintikkas knowledge and belief. Logic and philosophy of logic bibliography philpapers. We present a family of quantified epistemic logics for reasoning about knowledge in multiagent systems. Quantifying in and other problems in first order epistemic logic. Cornell up, ithaca, ma, quantified epistemic logic employing the notion of a conceptual cover aloni phd thesis.
Roles, rigidity, and quantification in epistemic logic wesley h. While propositional logic can only express facts, autoepistemic logic can express knowledge and lack of knowledge about facts. In modern philosophy, however, epistemic logic is used as a technical term not only for the logic of knowledge but also for the logic of belief. Philosophy of logic is devoted to the investigation, analysis and reflection on issues arising in logic, while philosophical logic concerns questions about reference, truth, quantification, existence, entailment, predication, identity, modality, and necessity. The problem is that certain theorems of quantified modal logic suggest that everything is necessarily something. Obviously, by itself, tweak ing the formal apparatus of epistemic logic does not solve traditional epistemological problems. Modern treatment of epistemic logic began in the 1950s when some philosophers noticed as scholastics had done before them certain regularities in the logical behaviour of the concept of knowledge for example, that knowing a conjunction is equivalent to knowing all its conjuncts and began to systematize them. In this approach, the state of a distributed system is characterized using epistemic concepts, such as, the information available to.
Some have supposed that the individuals we talk about in epistemic logic are. Modal logic today is an enormously broader enterprise than it was in aristotles time. For a modern treatment of classic puzzles of quanti. Pdf a complete quantified epistemic logic for reasoning.
Holliday university of california, berkeley abstract this chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. Many epistemic logics are modal logics, whose language contains one or more knowledge operators and whose semantics is given in terms of. Moreover, they are also subject to theprinciples of modal duality. Quantified epistemic logics with flexible terms core. My work on epistemic logic developed from my research in artificial intelligence. A modala word that expresses a modalityqualifies a statement. We introduce quantified interpreted systems, a semantics to reason about knowledge in multiagent systems in a firstorder setting. An introduction to logics of knowledge and belief arxiv. Transition semantics turns out to be an adequate tool to account for the distinctions introduced. Roles, rigidity, and quantification in epistemic logic uc berkeley. Despite its various successful applications in theoretical computer science, ai, and game theory, the technical development of the field has been mainly focusing on the propositional part, i. Outline of a logic of knowledge of acquaintance analysis. Philosophy of logic, the study, from a philosophical perspective, of the nature and types of logic, including problems in the field and the relation of logic to mathematics and other disciplines the term logic comes from the greek word logos.
The article also gives the logic of an alternative version, the dependent ramsey test, according to which a conditional is accepted just in case i the consequent is accepted if the belief state is revised by the antecedent and ii the consequent is rejected e. Knowingwho in quantified epistemic logic springerlink. And therefore without much exaggeration or distortion we can say that to articulate the logic of this notion of modality was modal logics original aim. If someone interested in the rules of the game asked you which card is the winning card. The language enjoys flexible terms with different denotations depending on the epistemic context in which they are interpreted. Knowingwho in quantified epistemic logic maria aloni. Philosophy of logic, the study, from a philosophical perspective, of the nature and types of logic, including problems in the field and the relation of logic to mathematics, computer science, the empirical sciences, and human disciplines such as linguistics, psychology, law, and education. As such the book covers a tremendous amount of material including some basic metalogic for propositional and predicate logic, modal propositional logic, quantified modal logic, tense logic, deontic logic, three valuedlogic, intuitionistic logic. And it manages all this in a rather skimpy 280 pages. We introduce epistemic quantified boolean logic eqbl, an extension of propositional epistemic logic with quantification over propositions. Quantified epistemic logics for reasoning about knowledge. Modal logic epistemic logic eric pacuit university of maryland, college park ai.
Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by hintikka 58. A semantics for quantified modal logic is presented that is based on kleenes notion of realizability. The term epistemic logic is often applied also to logics of related notions, such as logics of belief more strictly, doxastic logics and justification. However because of the serial property ofs5 andkd45 models, a. Roles, rigidity, and quantification in epistemic logic. In this paper, we adapt that model theory to treat quantified modal logics. Lecture notes modal logic linguistics and philosophy. Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. In contemporary epistemology, it is common to distinguish between three kinds of knowledge see, e. Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. No previous exposure to epistemic logic is assumed. The autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the. Speaking roughly, these are i cases of knowledge in which a cognitive agent s knows that something is true for example, that the earth revolves.
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