This paper shows that a collection of modal relevant logics are conservatively extended by the ad... more This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.
In Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semanti... more In Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator`It is supererogatory that'. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation,. For worlds u; v and w, we s a y that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics`DWE' for`Doing Well Enough'.
This proof would not be well received. But it is valid, in fact sound, on the classical logicians... more This proof would not be well received. But it is valid, in fact sound, on the classical logicians' definition. The premise cannot be true in any possible circumstance in which the conclusion is false. For the conclusion is necessarily true. And the premise is true. Thus the argument ...
This paper presents ConR ('Conditional R'), a logic of conditionals based on Anderson and Belnap'... more This paper presents ConR ('Conditional R'), a logic of conditionals based on Anderson and Belnap's system R. A Routley-Meyer-styte semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, 'A Relevant Theory of Conditionals' (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis' theory of causation, Lewis' dyadic deontic logic, and Chellas' dyadic deontic logic•
英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several auth... more 英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several authors have examined Russell's reification of forms from the point of view of their role in the multiple relation theory of judgment. But logical forms are also supposed to play ...
This paper begins by arguing that a truth conditional approach to the semantics for relevant logi... more This paper begins by arguing that a truth conditional approach to the semantics for relevant logic is unnatural. Rather, we should adopt an informational semantics. On this view, the indices in the Routley-Meyer semantics are situations, which can be said either to contain or not contain, particular pieces of information. Valid inference, then, is seen as information preservation, not truth preservation. The distinction between truth and information gives us some freedom in our treatment of logic. For example, we may have a very classical theory of truth but a very non-clasisical theory of information. On the other hand, we may accept very non-classical theories of truth (such as dialetheism) together with an informational treatment of logic.
DURING THE 1950's and 1960's, Alan R. Anderson wrote a number of interesting and influential pape... more DURING THE 1950's and 1960's, Alan R. Anderson wrote a number of interesting and influential papers about the deontic logic.' The present paper is an attempt to amalgamate a variety of ideas from these papers to create a coherent single position.* In particular, from Anderson (1956/66) and (1958) I adopt his technique for reducing deontic logic to alethic modal logic. And I follow the suggestion of Anderson (1967) that a system that incorporates a relevant implication connective (in the sense of the Anderson-Belnap system R) be used to avoid certain difficulties that plague systems based on classical logic. I call this logic RTvmo because it is a monadic deontic logic based on the alethic modal relevant logic RT and incorporates a propositional constant V.
The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Mey... more The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Meyer semantics, can be given without using the Routley star operator to treat negation. In the resulting semantics, negation is treated implicationally. It is shown that, by ...
Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a ... more Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a closed subset which is an M0-set of Hausdorff h-measure 0. He asked whether the same result holds for M-sets. In the first paper under review, the authors provide a negative answer. ...
This paper shows that a collection of modal relevant logics are conservatively extended by the ad... more This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.
In Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semanti... more In Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator`It is supererogatory that'. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation,. For worlds u; v and w, we s a y that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics`DWE' for`Doing Well Enough'.
This proof would not be well received. But it is valid, in fact sound, on the classical logicians... more This proof would not be well received. But it is valid, in fact sound, on the classical logicians' definition. The premise cannot be true in any possible circumstance in which the conclusion is false. For the conclusion is necessarily true. And the premise is true. Thus the argument ...
This paper presents ConR ('Conditional R'), a logic of conditionals based on Anderson and Belnap'... more This paper presents ConR ('Conditional R'), a logic of conditionals based on Anderson and Belnap's system R. A Routley-Meyer-styte semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, 'A Relevant Theory of Conditionals' (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis' theory of causation, Lewis' dyadic deontic logic, and Chellas' dyadic deontic logic•
英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several auth... more 英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several authors have examined Russell's reification of forms from the point of view of their role in the multiple relation theory of judgment. But logical forms are also supposed to play ...
This paper begins by arguing that a truth conditional approach to the semantics for relevant logi... more This paper begins by arguing that a truth conditional approach to the semantics for relevant logic is unnatural. Rather, we should adopt an informational semantics. On this view, the indices in the Routley-Meyer semantics are situations, which can be said either to contain or not contain, particular pieces of information. Valid inference, then, is seen as information preservation, not truth preservation. The distinction between truth and information gives us some freedom in our treatment of logic. For example, we may have a very classical theory of truth but a very non-clasisical theory of information. On the other hand, we may accept very non-classical theories of truth (such as dialetheism) together with an informational treatment of logic.
DURING THE 1950's and 1960's, Alan R. Anderson wrote a number of interesting and influential pape... more DURING THE 1950's and 1960's, Alan R. Anderson wrote a number of interesting and influential papers about the deontic logic.' The present paper is an attempt to amalgamate a variety of ideas from these papers to create a coherent single position.* In particular, from Anderson (1956/66) and (1958) I adopt his technique for reducing deontic logic to alethic modal logic. And I follow the suggestion of Anderson (1967) that a system that incorporates a relevant implication connective (in the sense of the Anderson-Belnap system R) be used to avoid certain difficulties that plague systems based on classical logic. I call this logic RTvmo because it is a monadic deontic logic based on the alethic modal relevant logic RT and incorporates a propositional constant V.
The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Mey... more The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Meyer semantics, can be given without using the Routley star operator to treat negation. In the resulting semantics, negation is treated implicationally. It is shown that, by ...
Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a ... more Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a closed subset which is an M0-set of Hausdorff h-measure 0. He asked whether the same result holds for M-sets. In the first paper under review, the authors provide a negative answer. ...
This paper sets out a probabilist theory of logic revision and discusses some of its consequences... more This paper sets out a probabilist theory of logic revision and discusses some of its consequences and the philosophical challenges that if faces. The probability theory is semantic. It is built upon a model for a very weak logic (the logic of bounded lattices) but that has sub-models for a wide variety of other logical systems – modal logics, relevant logics, linear logics, other substructural logics, fuzzy logic, and so on. The probability theory used is itself non-classical, although in those regions of the model in which classical logic holds probabilities act classically. Suggestions are made as to the treatments of debate and negotiation about logical rules and about the problems of logical omniscience and the apriority of logic.
This paper is dedicated to Peter Schotch. During the year I spent at Dalhousie in the early 1990s... more This paper is dedicated to Peter Schotch. During the year I spent at Dalhousie in the early 1990s, Peter was going through an S1 phase. During that year, and afterwards, I spent many hours discussing possible semantics for S1 with Peter. This was also my first introduction to the philosophy of logic of C.I. Lewis. I found Peter's thoughts on this topic, as on all topics in logic and philosophy, full of interesting ideas, only some of which I really understood at the time. More recently, Peter and I have engaged in a discussion about Lewis's notion of entailment. This paper presents my side of that conversation.
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