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LINGUISTIX&LOGIK, Tony Marmo's blog
Sunday, 6 March 2005

Now Playing: COUNTERFACTUALS WEEK (REPOSTED)
Topic: PARACONSISTENCY

Using Counterfactuals in Knowledge-Based Programming


By Joseph Y. Halpern & Yoram Moses

Knowledge-based programs, first introduced by Halpern and Fagin [and further developed by Fagin, Halpern, Moses, and Vardi, are intended to provide a high-level framework for the design and specification of protocols. The idea is that, in knowledge-based programs, there are explicit tests for knowledge. Thus, a knowledge-based program might have the form
if K(x = 0) then y := y + 1 else skip,

where K(x = 0) should be read as "you know x = 0" and skip is the action of doing nothing. We can informally view this knowledge-based program as saying "if you know that x = 0, then set y to y + 1 (otherwise do nothing)".
Knowledge-based programs are an attempt to capture the intuition that what an agent does depends on what it knows. They have been used successfully (...) both to help in the design of new protocols and to clarify the understanding of existing protocols. However, as we show here, there are cases when, used naively, knowledge-based programs exhibit some quite counterintuitive behavior. We then show how this can be overcome by the use of counterfactuals. In this introduction, we discuss these issues informally, leaving the formal details to later sections of the paper.
Source: CLE

Posted by Tony Marmo at 00:01 GMT
Updated: Friday, 4 March 2005 19:06 GMT
Thursday, 3 March 2005

Topic: PARACONSISTENCY

Modulated Logics and Uncertain Reasoning


By Walter Carnielli & Maria Claudia C. Gracio

This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. We give an uniform treatment of modulated logics, obtaining some general results in model theory. Besides carefully reviewing the Logic of Ultrafilters and the Logic of Most, two new monotonic logical systems are introduced here: the Logic of Many and the Logic of Ubiquity, which formalize inductive assertions of the kind many and almost everywhere through new modulated quantifiers and, respectively. Although the notion of most can be captured by means of a modulated quantifier semantically interpreted by cardinal measure on sets of evidences, it is proven that this system, although sound, cannot be complete if checked against the intended model. This justifies the interest on a purely qualitative approach to this kind of quantification, what is guaranteed by interpreting the modulated quantifiers, respectively, as families of upper closed sets and pseudo-topologies. Modulated logics can be used to provide alternative foundations for fuzzy concepts and fuzzy reasoning, for reasoning on social choice theory, and for gaining a new regard on certain problems in philosophy of science.

Source: CLE

Posted by Tony Marmo at 00:01 GMT
Updated: Thursday, 3 March 2005 08:01 GMT
Saturday, 26 February 2005

Topic: PARACONSISTENCY

Resolving Contradictions : A Plausible Semantics for Inconsistent Systems


By Eliezer L. Lozinskii

The purpose of a Knowledge System S is to represent the world W faithfully. If S turns out to be inconsistent containing contradictory data, its present state can be viewed as a result of information pollution with some wrong data. However, we may reasonably assume that most of the system content still reflects the world truthfully, and therefore it would be a great loss to allow a small contradiction to depreciate or even destroy a large amount of correct knowledge. So, despite the pollution, S must contain a meaningful subset, and so it is reasonable to assume (as adopted by many researchers) that the semantics of a logic system is determined by that of its maximally consistent subsets, mc-subsets. The information contained in S allows deriving certain conclusions regarding the truth of a formula F in W. In this sense we say that S contains a certain amount of semantic information, and provides an evidence of F. A close relationship is revealed between the evidence, the quantity of semantic information of the system, and the set of models of its mc-subsets. Based on these notions, we introduce thesemantics of weighted mc-subsets as a way of reasoning in inconsistent systems. To show that this semantics indeed enables reconciling contradictions and deriving plausible beliefs about any statement including ambiguous ones, it is successfully applied to a series of justifying examples, such as chain proofs, rules with exceptions, and paradoxes. (Go on)

Posted by Tony Marmo at 00:01 GMT
Updated: Saturday, 26 February 2005 13:39 GMT
Saturday, 15 January 2005

Topic: PARACONSISTENCY
I ask the Paraconsistent Logicians that happened upon this blog to comment on the paper below with special attention, and write their thoughts.

On Partial and Paraconsistent Logics


By Reinhard Muskens

In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap's and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants.

Source: Semantics Archive
See it

Posted by Tony Marmo at 00:01 GMT
Updated: Saturday, 15 January 2005 15:33 GMT
Monday, 10 January 2005

Now Playing: REPOSTED
Topic: PARACONSISTENCY

The Inconsistency View on Vagueness


By Matti Eklund

I elaborate and defend the inconsistency view on vagueness I have earlier argued for in my (2002) and (forthcoming). In rough outline, the view is that the sorites paradox arises because tolerance principles, despite their inconsistency, are meaning-constitutive for vague expressions. Toward the end of the paper I discuss other inconsistency views on vagueness that have been proposed, and compare them to the view I favor.

See it

Posted by Tony Marmo at 00:01 GMT
Updated: Thursday, 6 January 2005 19:02 GMT
Saturday, 8 January 2005

Now Playing: REPOSTED
Topic: PARACONSISTENCY

A Positive Formalization
for the Notion of Pragmatic Truth


By Tarcisio Pequeno, Arthur Buchsbaum & Marcelino Pequeno

A logic aimed to formalize the concept of pragmatic truth is presented. We start by examining a previous attempt of formalization by da Costa and collaborators, reported in Mikenberg, da Costa, and Chuaqui (1986), da Costa, Chuaqui, and Bueno (1996) and da Costa, Bueno and French(1998). However, their formalization works as mere possibility in face of what is known, or assumed. It is pointed out here that not being in conflict with the assumed knowledge is not enough to regard a proposition as a truth of any sort, providing just a necessary condition.
A typical picture of the way a scientific theory evolves exhibit alternative hypothesis competing for expanding the theory. In our view, a pragmatic knowledge, at this stage of development of the theory, is one that can be taken as true under all those competing hypothesis. The logic presented here formalizes this process of theory evolution in order to properly express the notion of pragmatic truth as we understand it.

View as html
Try pdf

Posted by Tony Marmo at 00:01 GMT
Updated: Saturday, 8 January 2005 13:12 GMT
Saturday, 6 November 2004

Topic: PARACONSISTENCY

Routes to Triviality


By Susan Rogerson and Greg Restall

It is well known that contraction-related principles trivialise naive class theory. It is less well known that many other principles unrelated to contraction also render the theory trivial. This paper provides a characterisation of a large class of formulas which do the job. This class includes all properly implication formulas known in the literature, and adds countably many more.

Follow this route to the paper

Posted by Tony Marmo at 00:01 GMT
Updated: Saturday, 6 November 2004 00:18 GMT
Thursday, 4 November 2004

Topic: PARACONSISTENCY

A QUESTION TO THE DEFLATIONISTS



As always, I shall try to be as concise as possible. (1) below is a classic principle of Logic:

(1) T(S) iff F(~S)


Still, given that in classic logic (2) is valid:

(2) if F(B) then T(A)


By (1) and (2), and by substituting ~S for B and S for A in (2), it is not obvious that (3) is blocked:

(3) if ~S then S


Thus, a sentence like (4) should make sense in a human language:

(4)#If Marilyn Monroe did not pass out then she passed out.


But (4) is nonsensical in English or in other natural language. There are several manners to fix (4) in a natural language like English:

(5)
a. If it is false that Marilyn Monroe did not pass out then it is true that she passed out.
b. If it is false that Marilyn Monroe did not pass out then she passed out.


And there are other ways not to fix it:

(6) #If Marilyn Monroe did not pass out then it is true that she passed out.


(7) below is the main deflationist claim:

(7) Adding it is true that to a sentence S adds nothing to its content.


(7) can explain why there is no difference of status between (5a) and (b), and why (6) cannot be an option to (4).

On the other hand, given that (8) below is not valid:

(8) if T(B) then F(A)


One should not expect (9) to be ok:

(9) If it is that true Marilyn Monroe did not pass out then it is false that she passed out.


But (9) is sensible in a natural language like English. Of course, in such case one might argue that, unlike in an artificial language, English if... so constructions might be interpreted as if and only if statements in some cases like (10), in the context of a mother talking to her daughter:

(10) If you break another vase in the house, you will have no ice cream tonight.


Where the daughter does not expect to be punished in the event that no vase is broken in the house. But (4), (9) and (10) are precisely the kind of evidences used to argue that natural languages are not semantically closed, i.e., they do not abide by (1) in all instances.

But if one dispenses with (1) in the case of natural language semantics, how can one maintain (7) or explain the cases where the sensical/ non-sensical status is not altered by the addition of it is true that ...?

Before advancing any proposal of my own, I would like to hear your thoughts on this matter.

Posted by Tony Marmo at 03:14 GMT
Updated: Thursday, 4 November 2004 09:57 GMT
Thursday, 28 October 2004

Topic: PARACONSISTENCY

Is the Liar Sentence Both True and False?


By Hartry Field

The argument with which I began shows that if we want to disbelieve instances of excluded middle (in the sense of, believe their negations) then we should be dialetheists (not merely that we should accept paraconsistent logics for some purposes). And as Priest has often urged. the most familiar arguments against the coherence of dialetheism are seriously faulty, a result of a refusal to take the doctrine seriously.

To appear in Beall and Armour-Garb, eds., Deflationism and Paradox (Oxford University Press 2004)

See it

Posted by Tony Marmo at 00:01 BST
Updated: Thursday, 28 October 2004 04:27 BST
Sunday, 24 October 2004

Topic: PARACONSISTENCY

Chunk and Permeate, a Paraconsistent Inference Strategy.
Part I: The Infinitesimal Calculus



By Bryson Brown & Graham Priest

In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind -specifically concerning the preservation of the consistency of each chunk -and concludes with some other possible applications and technical questions.

Keywords:
chunking, infinitesimal calculus, paraconsistent logic

Published version (For Subscribers of the Journal of Philosophical Logic)


Posted by Tony Marmo at 00:01 BST
Updated: Sunday, 24 October 2004 12:14 BST
Wednesday, 20 October 2004

Topic: PARACONSISTENCY

Dialetheism, logical consequence and hierarchy


By Bruno Whittle

Dialetheism is defined by Graham Priest to be the view that there are true contradictions. It is supposed to offer treatments of the semantic paradoxes that avoid the problems faced by more orthodox resolutions. The advantage of these treatments is supposed to be that they avoid the sort of appeal to a hierarchy of languages or concepts that more orthodox resolutions seem invariably to have to make. For since a dialetheist can simply accept as sound the derivations of contradictions involved in the paradoxes, there is no need for him to invoke a hierarchy to block these derivations.

In this article I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

In ?1 I explain why and how a dialetheist needs to be able to talk about logical consequence. In ?2 I argue that there are in fact severe restrictions upon how exactly a dialetheist can talk about logical consequence. These restrictions stem from a version of Curry's paradox. I then argue in ?3 that a dialetheist must appeal to a hierarchy of concepts of logical consequence, and, further, that each of these concepts is dialetheically unobjectionable. The justification of this latter claim involves proving that the addition of these concepts together with natural rules for them conservatively extends dialetheic logic. This is proved in the appendix.

Read this article

Posted by Tony Marmo at 00:01 BST
Updated: Wednesday, 20 October 2004 04:23 BST
Friday, 15 October 2004

Topic: PARACONSISTENCY

DA COSTA AND PRIEST ONLINE PAPERS




Please, if anyone has a website with online copies of all works by Newton da Costa and Graham Priest, let me know.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 15 October 2004 03:39 BST
Monday, 11 October 2004

Topic: PARACONSISTENCY

Coherentism and Justified Inconsistent Beliefs: A Solution


By Jonathan Kvanvig

Problems for coherentism come in two forms. The fundamental issue that coherentists have not been very successful in addressing is the problem of saying precisely what coherence involves. BonJour's account in The Structure of Empirical Knowledge is among the most detailed available, but he admits that it "is a long way from being as definitive as desirable." More recently, he has been more skeptical about the accomplishments on this score to date, writing that "the precise nature of coherence remains an unsolved problem." Recently, some hope has emerged that progress can be made on this issue, but the more pressing problem for coherentism comes in the form of objections to the view that are independent of any particular construal of the coherence relation itself. These problems are more pressing, since if these objections are correct, coherentists need not waste their time explicating the nature of coherence-the view would be false independently of these details. Among these objections are the claims that coherentism cannot account for the essential role of experience in justification (commonly termed the isolation objection), that coherentism cannot correctly explain what it is to base one's beliefs properly, and that coherentism cannot explain properly the relationship between justification and truth. My view of the matter is that none of these objections decisively undermine coherentism, but there is a one version of the problem of the relationship between justification and truth that is, to my mind, the most pressing difficulty coherentism faces. It is the problem of justified inconsistent beliefs. In a nutshell, there are cases in which our beliefs appear to be both fully rational and hence justified, and yet the contents of the beliefs are inconsistent, often knowingly inconsistent. This fact contradicts the seemingly obvious idea that a minimal requirement for coherence is logical consistency.

I will first explain the problem of justified inconsistent beliefs for coherentism, and then show how to avoid it. To anticipate my argument, the key is to note that there are distinct types of justification. There is the ordinary intuitive notion on which justification is roughly synonymous with reasonable or rational belief. Coherentists, however, are interested in the type of justification that is part of a proper account of knowledge, the kind of justification which is such that if it is ungettiered and conjoined to true belief, yields knowledge. In slogan form, I will summarize this idea as by saying that the kind of justification in question for coherentists is the kind that puts one in a position to know. I will call such justification "epistemic justification", and when I intend to talk about the more ordinary, commonplace justification that need not put one in a position to know, I will use the term `justification' without the qualifier. I will argue, in my preferred terminology, that epistemic justification cannot be identified with justification. The key to solving the problem of justified inconsistent beliefs, then, is to allow that they are possible on the ordinary intuitive notion of justification but not on the kind of justification that puts one in a position to know. The trick is to substantiate these claims and not rely simply on the claim that such a distinction can be drawn. I will do so with little more in the way of assumptions than a relatively well-understood form of internalism, something coherentists (and others) are committed to, anyway.


Continue

Posted by Tony Marmo at 00:01 BST
Updated: Monday, 11 October 2004 10:28 BST
Sunday, 3 October 2004

Topic: PARACONSISTENCY

Reactive Kripke Semantics and Arc Accessibility


Dov Gabbay
Source: CLE (CombLog'04)

Ordinary Kripke models are not reactive. When we evaluate (test/measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This paper studies Kripke models which react to the evaluation process and change themselves during the process.
This is reminiscent of game theoretic semantics where the two sides react to each other. However, reactive Kripke models do not go as far as that. The only additional device we add to Kripke semantics to make it reactive is to allow the accessibility relation to access itself. Thus the accessibility relation R of a reactive Kripke model contains not only pairs (a, b) belongs to Rof possible worlds (b is accessible to a, i.e. there is an accessibility arc from a to b) but also pairs of the form (t, (a, b)) belongs to R, the arc (a, b) is accessible to t.This new kind of Kripke semantics allows us to characterise more axiomatic modal logics (with one modality) by a class of reactive frames. There are logics which cannot be characterised by ordinary frames but which can be characterised by reactive frames. We use such models to fibre logics which disagree on their common language.


Get it

Posted by Tony Marmo at 06:01 BST
Sunday, 26 September 2004

Topic: PARACONSISTENCY

Logics of Imperfect Information


by Gabriel Sandu
Source CLE

The paper contains a survey of results and interpretations of incomplete information in predicate and modal logics.

Download


Posted by Tony Marmo at 01:01 BST
Updated: Friday, 24 September 2004 03:57 BST

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