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On Epistemic Logic with Justification
- NATIONAL UNIVERSITY OF SINGAPORE
, 2005
"... The true belief components of Plato's tripartite definition of knowledge as justified true belief are represented in formal epistemology by modal logic and its possible worlds semantics. At the same time, the justification component of Plato's definition did not have a formal representat ..."
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Cited by 26 (9 self)
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The true belief components of Plato's tripartite definition of knowledge as justified true belief are represented in formal epistemology by modal logic and its possible worlds semantics. At the same time, the justification component of Plato's definition did not have a formal representation. This
A note on some explicit modal logics
- Proceedings of the Fifth Panhellenic Logic Symposium
, 2005
"... Abstract. Artemov introduced the Logic of Proofs (LP) as a logic of explicit proofs. We can also offer an epistemic reading of this formula: “t is a possible justification of φ”. Motivated, in part, by this epistemic reading, Fitting introduced a Kripke style semantics for LP in [8]. In this note, w ..."
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Cited by 20 (0 self)
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Abstract. Artemov introduced the Logic of Proofs (LP) as a logic of explicit proofs. We can also offer an epistemic reading of this formula: “t is a possible justification of φ”. Motivated, in part, by this epistemic reading, Fitting introduced a Kripke style semantics for LP in [8]. In this note, we prove soundness and completeness of some axiom systems which are not covered in [8]. 1
Logical omniscience and common knowledge: What do we know and what do we know
- National University of Singapore
, 2005
"... Abstract: Two difficult issues for the logic of knowledge have been logical omniscience and common knowledge. Our existing logics of knowledge based on Kripke structures seem to justify logical omniscience, but we know that in real life it does not exist. Also, common knowledge appears to be needed ..."
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Cited by 10 (4 self)
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Abstract: Two difficult issues for the logic of knowledge have been logical omniscience and common knowledge. Our existing logics of knowledge based on Kripke structures seem to justify logical omniscience, but we know that in real life it does not exist. Also, common knowledge appears to be needed for certain real life procedures to work. But it seems quite implausible that it actually exists in real people. We suggest two procedure based semantics for knowledge which seem to take care of both these issues in a relatively realistic way. What this suggests is that if we really want to understand knowledge, then existing customs and plans must play a greater role than we are used to assigning them. 1
Sentences belief and logical omniscience or what does deduction tell us
- Review of Symbolic Logic
, 2008
"... Abstract. We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to ..."
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Cited by 4 (1 self)
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Abstract. We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning to beliefs in general contexts, including the context of animal belief (where action is usually our only clue to a belief), and of human belief which is expressed in language. §1. Introduction. In deductive reasoning, if φ is deduced from some set Ɣ, then φ is already implicit in Ɣ. But then how do we learn anything from deduction? That we do not learn anything is the (unsatisfying) answer suggested by Socrates in Plato’s Meno. This problem is echoed in the problem of logical omniscience prominent in epistemic logic according to which an agent knows all the consequences of his/her knowledge. An absurd
Sentences, Propositions and Logical Omniscience, or What does Deduction tell us
- the Review of Symbolic Logic
"... Abstract: In deductive reasoning, if φ is deduced from some set Γ, then φ is already implicit in Γ. But then how do we learn anything from deduction? That we do not learn anything is the (unsatisfying) answer suggested by Socrates in Plato’s Meno. This problem is echoed in the problem of logical omn ..."
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Abstract: In deductive reasoning, if φ is deduced from some set Γ, then φ is already implicit in Γ. But then how do we learn anything from deduction? That we do not learn anything is the (unsatisfying) answer suggested by Socrates in Plato’s Meno. This problem is echoed in the problem of logical omniscience prominent in epistemic logic according to which an agent knows all the consequences of his/her knowledge. An absurd consequence is that someone who knows the axioms of Peano Arithmetic knows all its theorems. Since knowledge presumes belief, the lack of closure of (actual) beliefs under deduction remains an important issue. The post-Gettier literature has concentrated on the gap between justified true belief and knowledge, but has not concerned itself with what belief is. This question, or at least an analysis of sentences of the form Jack believes that frogs have ears, has been prominent in the philosophy of language. But even there, less attention has been paid to how we know what someone believes. This turns out to matter.
On Proof Realization on Modal Logic
, 2009
"... Artemov’s Logic of Proof, LP, is an explicit proof counterpart of S4. Their formal connection is built through the realization theorem, that every S4 theorem can be converted to an LP theorem by substituting proof terms for provability modals. Instead of the realization of theorems, what is concerne ..."
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Artemov’s Logic of Proof, LP, is an explicit proof counterpart of S4. Their formal connection is built through the realization theorem, that every S4 theorem can be converted to an LP theorem by substituting proof terms for provability modals. Instead of the realization of theorems, what is concerned in this paper is the realization of proofs. We will show that only a subclass of S4 proofs, called non-circular proofs, can be realized as LP proofs in this way. Furthermore, we introduce a numerical version of LP, called S4 ∆ , to constructively prove that every S4 theorem has a non-circular proof. These results provide a new algorithmic proof of the realization theorem. 1
Comments on the Logic of Justification
, 2013
"... This note presents some comments and questions related to two papers of Sergei Artemov: ..."
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This note presents some comments and questions related to two papers of Sergei Artemov:
