Off-campus access
Using PhilPapers from home?
Click here to configure this browser for off-campus access.
- Melvin Fitting, Justification Logics, Logics of Knowledge, and Conservativity.Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open.
Similar books and articles
We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.
Reading list
| Discuss | Edit | Categorize | My bibliography
| Export citation | Other links: springerlink.com dx.doi.org | Scholar | At my library | More options ...
| | Other links: springerlink.com dx.doi.org | Scholar | At my library | More options ... This paper is devoted to showing certain connections between normal modal logics and those strictly regular modal logics which have as a theorem. We extend some results of E. J. Lemmon (cf. [66]). In particular we prove that the lattice of the strictly regular modal logics with the axiom is isomorphic to the lattice of the normal modal logics.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: jstor.org | Scholar | At my library | More options ...
| | Other links: jstor.org | Scholar | At my library | More options ... Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: jstor.org | Scholar | At my library | More options ...
| | Other links: jstor.org | Scholar | At my library | More options ... This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic called LP, introduced by Sergei Artemov [1, 3], which formed the central part of a project to provide an arithmetic semantics for propositional intuitionistic logic. The project was successful, but there was a considerable bonus: LP came to be understood as a logic of knowledge with explicit justifications and, as such, was capable of addressing in a natural way long-standing problems of logical omniscience. Since then, LP has become one member of a family of related logics, all logics of knowledge with explicit knowledge terms. In this paper the original problem of intuitionistic foundations is discussed only briefly. We concentrate entirely on issues of reasoning about knowledge.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: springerlink.com dx.doi.org jstor.org | Scholar | At my library | More options ...
| | Other links: springerlink.com dx.doi.org jstor.org | Scholar | At my library | More options ... This papers gives a survey of recent results about simulations of one class of modal logics by another class and of the transfer of properties of modal logics under extensions of the underlying modal language. We discuss: the transfer from normal polymodal logics to their fusions, the transfer from normal modal logics to their extensions by adding the universal modality, and the transfer from normal monomodal logics to minimal tense extensions. Likewise, we discuss simulations of normal polymodal logics by normal monomodal logics, of nominals and the difference operator by normal operators, of monotonic monomodal logics by normal bimodal logics, of polyadic normal modal logics by polymodal normal modal logics, and of intuitionistic modal logics by normal bimodal logics.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: springerlink.com dx.doi.org jstor.org | Scholar | At my library | More options ...
| | Other links: springerlink.com dx.doi.org jstor.org | Scholar | At my library | More options ... Among non-monotonic systems of reasoning, non-monotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been established concerning these logics. In this paper we introduce non-monotonic modal logics based on many-valued logics, rather than on classical logic. This extends earlier work of ours on many-valued modal logics. Intended applications are to situations involving several reasoners, not just one as in the standard development.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since justification logics are newer and less well-known than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Justification logics are logics of knowledge in which explicit reasons are formally represented. Standard logics of knowledge have justification logic analogs. Connecting justification logics and logics of knowledge are Realization Theorems. In this paper we give a new, constructive proof of the Realization Theorem connecting S5 and its justification analog, JS5. This proof is, I believe, the simplest in the literature.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Several justification logics have evolved, starting with the logicLP, (Artemov 2001). These can be thought of as explicit versions of modal logics, or logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. Modal logics come in various strengths. For their corresponding justification logics, differing strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Discussion of Melvin Fitting, Justification logics, logics of knowledge, and conservativity
 Back
All discussions
Start a new thread
|
There are no threads in this forum |
Nothing in this forum yet.
