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LINGUISTIX&LOGIK, Tony Marmo's blog
Monday, 6 September 2004



Roman Tuziak

Paraconsistent logic was introduced in order to provide the framework for inconsistent but nontrivial theories. It was initiated by J. Lukasiewicz (1910) in Poland and, independently, by N. A. Vasilev (1911-13) in Russia, but only in 1948 the first paraconsistent formal system was designed. Since then thousands of papers have been published in this field. Paraconsistency became one of the fastest growing branches of logic, due to its fruitful applications to computer science, information theory, and artificial intelligence. K. R. Popper touched on the problem in his paper ,,What is Dialectic?" (1940). Although only mentioned, his basic idea of the possibility of a formal system of such a logic was fresh and original. Another attempt of exploring the logic of contradiction, this time as a dual to intuitionistic logic, was made by Popper in his paper ,,On the Theory of Deduction I and II" (1948). The same idea was formalized by N. D. Goodman (1981) and developed by D. Miller (1993) under a label ,,Logic for Falsificationists".
Popper`s contribution to the subject of paraconsistent logic has not been properly recognized so far. Since Lukasiewicz`s and Vasilev`s works were still not translated into any West European languages in the 1940s, he should be undoubtedly regarded as an independent forerunner of paraconsistency. On the other hand, it seems tempting to adapt some of Popper`s other ideas for the theory of paraconsistent logic (the way it was done with Vasilev`s very general concepts) and, especially, for the theory of artificial intelligence.


Posted by Tony Marmo at 14:46 BST
Sunday, 5 September 2004


Paraconsistent Logics and Paraconsistency:
Technical and Philosophical Developments

by Newton C. A. da Costa, D?cio Krause & Ot?vio Bueno

Saying in a few words, paraconsistent logics (PL) are the logics that can be the logics of inconsistent but non-trivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. Roughly speaking, in a trivial theory 'everything' (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems like intuitionistic logic, inconsistency entails triviality, and conversely. So, how can we speak of inconsistent but non trivial theories? Of course by exchanging the underlying logic to one which may admit inconsistency without making the system trivial. Paraconsistent logics do the job.
Let us remark that our use of terms like 'consistency', 'inconsistency', 'contradictory' and similar ones is syntactical, what is in accord with the original metamathematical terminology of Hilbert and his school. On the other hand, in order to treat such terms from the semantical point of view, in the field of paraconsistency, one must be able to build, for instance, a paraconsistent set theory beforehand. This is possible, as we shall see, although most semantics for paraconsistent logics are classical, i.e., constructed inside classical set theories. So, the best, to begin with, is to employ the above terms syntactically.

Source: CLE


See also:

Science and Partial Truth - A Unitary Approach to Models and Scientific Reasoning

by Newton C. A. da Costa & Steven French

Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

Check it

Posted by Tony Marmo at 01:01 BST
Updated: Sunday, 5 September 2004 13:56 BST
Saturday, 4 September 2004


Towards a Logic for Pragmatics. Assertions and Conjectures

by Gianluigi Bellin and Corrado Biasi

The logic for pragmatics extends classical logic in order to characterize the logical properties of the operators of illocutionary force such as that of assertion and obligation and of the pragmatic connectives which are given an intuitionistic interpretation. Here we consider the cases of assertions and conjectures : the assertion that a mathematical proposition _ is true is justified by the capacity to present an actual proof of _, while the conjecture that _ is true is justified by the absence of a refutation of _. We give sequent calculi of type G3i and G3i m inspired by Girard's LU , with subsystems characterizing intuitionistic reasoning and some forms of classical reasoning with such operators. Extending Godel, McKinsey, Tarski and Kripke's translations of intuitionistic logic into S4 , we show that our sequent calculi are sound and complete with respect to Kripke's semantics for S4 .


See also
G. Bellin and Corrado Biasi.
Cut-Elimination for the logic of pragmatics
(This is work in progress, which summarizes dr Corrado Biasi's Tesi di Laurea. It substantially refines and develops the ideas and the direction of research presented at the IMLA-FLOC'02 conference.)


Posted by Tony Marmo at 01:01 BST
Updated: Saturday, 4 September 2004 12:03 BST
Friday, 3 September 2004


Modal Predicates

Andrea Iacona

Despite the wide acceptance of standard modal logic, there has always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators. The aim of the formal model outlined in this paper is to capture what I take to be the only plausible sense in which `possible' and `necessary' can be treated as predicates. The model is built by enriching the language of standard modal logic with a quantificational apparatus that is "substitutional" rather than "objectual", and by obtaining from the language so enriched another language in which constants for such predicates apply to singular terms that stand for propositions.


Posted by Tony Marmo at 14:38 BST
Updated: Friday, 3 September 2004 14:39 BST
Thursday, 2 September 2004

Topic: Notes on Pirah?

Note #2


Cultural Constraints on Grammar and Cognition in Pirah?: Another Look at the Design Features of Human Language

Page 10

However, there are two words, usually occurring in reference to an amount eaten or desired, which by their closest translation equivalents, 'whole' b?aiso and 'part' g?i?i might seem to be quantifiers:
(19) a. t?ob?hai hi b? -a -i -so kohoai-s?og -ab -aga?
child 3 touch -causative -connective -nominalizer 'whole' eat -desiderative -stay -thus
'The child wanted/s to eat the whole thing.'
(lit: 'Child muchness/fullness eat is desiring.')
b. t?ob?hai hi g?i -?i kohoai-s?og-ab -aga?
child 3 that -there eat -desiderative 'part' (in the appropriate context) -stay -thus
'The child wanted/s to eat a piece of the thing.'
(lit: 'Child that there eat is desiring.')

In (19) b?aiso and g?i?i are used as nouns. But they can also appear as
postnominal modifiers:
(20) a. t?ob?hai hi pooga?hia? b?aiso kohoai-s?og -ab -aga?
child 3 banana whole eat- desiderative -stay -thus
'The child wanted/s to eat the whole banana.'
(lit: 'Child banana muchness/fullness eat is desiring.')
b. t?ob?hai hi pooga?hia? g?i?i kohoai-s?og-ab -aga?
child 3 banana piece eat -desiderative -stay -thus
'The child wanted/s to eat part of the banana.'
(lit: 'Child banana piece eat is desiring.')

Whether a pair of items are quantifiers or not depends firstly on the theoretic assumptions made. There is no way to say whether b?aiso and g?i?i are real quantifiers or not just by giving examples in a non-theoretic fashion. In any case, it is not uncommon to find words that appear in different positions both as nouns and nominal modifiers. That is a common fact of languages around the world and not any special or unique feature of Pirah?.

Aside from their literal meanings, there are important reasons for not interpreting these two words as quantifiers. First, their Truth Conditions are not equivalent to those of real quantifiers.

This is tricky. A sentence may be true or false in a given situation/world, but it cannot be assumed that speakers will produce only true sentences in a given context. False sentences, which are completely grammatical, may be and often are produced.

For example, consider the contrast in (21) vs. (22):
Context: Someone has just killed an anaconda. Upon seeing it, (21a) below is uttered. Someone takes a piece of it. After the purchase of the remainder, the content of (21a) is reaffirmed as (21b):
(21) a. 7?o?i hi pa?hoa7a? 7iso? b?aiso 7oaboi -ha?
foreigner 3 anaconda skin 'whole' buy -relative certainty
'The foreigner will likely buy the entire anaconda skin.'
b. 7ai? hi b?aiso 7oaob -?h?; hi 7ogi? 7oaob -?h?
affirmative 3 whole buy -complete certainty 3 bigness buy complete certainty
'Yes, he bought the whole thing.'

Now, compare this with the English equivalent, where the same context is
(22) a. STATEMENT: He will likely buy the whole anaconda skin.
b. OCCURRENCE: Piece is removed (in full view of interlocutors).
c. STATEMENT: %He bought the whole anaconda skin.

It simply would be dishonest and a violation of the meaning of 'whole' to utter it
in (22b). But this is not the case in Pirah?, (21b).
Page 11

However in (21b) the term b?aiso is not used alone. 7ogi?, he term for bigness, as Everett calls it, is present as well. This suggests that a literal translation of (21b) would be Yes, he bought a majority of the whole thing, regardless of whether the sentence is true or false in the context where it is uttered. The expression a majority of the whole exists in English and other languages and means a part (the larger part) and not the whole.

Posted by Tony Marmo at 14:29 BST
Updated: Thursday, 2 September 2004 14:31 BST
Wednesday, 1 September 2004

Topic: Notes on Pirah?
As suggested by RdR and others, I shall be writing small notes on Daniel Everett's work, i.e., about the analyses he makes of Pirah? data.

Note #1


Cultural Constraints on Grammar and Cognition in Pirah?: Another Look at the Design Features of Human Language

page 7

Some examples which show how Pirah? expresses what in other cultures would
be numerical concepts:
(10) a. t? 7?t?i7isi h?i hii 7aba7??gio 7oogabaga?
1 fish small pred. only want
'I only want {one/a couple/a small} fish.'
(NB: This could not be used to express a desire for one fish that was very large, except as a joke.)

Interesting. In Portuguese we may have parallel examples:

(10') a. Eu quero um pouco de peixe.

(10') may be translated as I want some fish or a little bit of fish. Indeed (10') may be interpreted as:

I want a small fish.
I want only one fish.
I want a small quantities of fish.
I want only a piece of a fish.

Of course, (10') cannot be used in the context where the speaker wants one very large fish.

Page 8

Interestingly, in spite of its lack of number and numerals, Pirah? superficially
appears to have a count vs. mass distinction:
(12) a. 7ao?i 7aa?b?i 7ao7aag? 7o? kapi?7io
foreigner many exist jungle other
'There are many foreigners in another jungle.'
b. */? 7ao?i 7apag? 7ao7aag? 7o? kapi?7io
foreigner much exist jungle other
? 'There are much foreigners in another jungle.'
(13) a. 7?ga?si7apag? 7ao7aag? 7o? kapi?7io
manioc meal much exist jungle other
'There is a lot of manioc meal in another jungle.'
b. *7?ga?si 7aa?b?i 7ao7aag? 7o? kapi?7io
manioc mealmany exist jungle other
*'There is many manioc meal in another jungle.'

However, this distinction is more consistently analyzed as the distinction between things that can be individuated and things that cannot, thus independent of the notion of counting.

It is impossible to conclude that some mind has the notion of individuation, but lacks the concept of unity. The sentences about are without any doubt instances of mass versus count nouns. To affirm otherwise is not consistent with the data presented.

Posted by Tony Marmo at 13:30 BST
Updated: Thursday, 2 September 2004 14:33 BST
Monday, 30 August 2004
Hara on Implicature and Attitude Predicates

Implicature Computation and Attitude Predicates

By Yurie Hara

The Handout (Source: The Semantics Archive)

The traditional view of Pragmatics:
Pragmatics is independent of syntax and semantics.
The output of syntactic and semantic computation is passed on to the pragmatic system.
Example: Scalar implicatures
Traditional view:
Implicatures are introduced after the whole computation of syntax and semantics is done.
Chierchia (2001):
Implicatures are generated locally and projected compositionally
Today's talk [see the link to the handout]:
mostly along with Chierchia. However, implicature computation takes place at where a proposition is combined with an attitude predicate.

The Article

Chierchia (2001) has proposed that implicatures are generated locally and projected compositionally. Implicatures induced by Japanese Contrastive Topic provide evidence for the local computation of implicature; however, their properties are not fully compatible with Chierchia's analysis. This paper shows that implicature computation should take place in a larger cycle than Chierchia's, namely at the position where a proposition is combined with an attitude predicate. The analysis mirrors Heim's (1992) theory on presupposition projection.
Japanese Contrastive Topics always induce implicatures. In other words, Contrastive Topic wa (as in (1)) is licensed under the situation where something else is implicated. The same implicature will arise when the sentence is not wa-marked (Nanninka-ga kita. `Some people-Nom came' will also implicates "Not everyone came." as a conversational scalar implicature). The difference between wa-marked and nonwa- marked is clearer in (2). The wa-induced implicature is conventional and hence obligatory (as in (2a)), whereas the non-wa-marked one is conversational and defeasible (as in (2b); see Hara (To appear) for the detailed discussion). Hara (2004) proposes that wa seeks for a stronger scalar alternative. This property is depicted as a presuppositional requirement ((3b); x is an attitude-bearer, B is a background and T is a topical element; see Hara (2004) for the comparison of this analysis with B?uring (1997)). For example, (1) implicates the speaker's uncertainty of the stronger (more informative) alternative, `Everyone came'. (2a) is infelicitous since the asserted proposition `Everyone came' is the strongest among the alternatives (`Some people came', `Most people came' etc.), and thus there is no room to implicate.

Download article


Posted by Tony Marmo at 01:01 BST
Updated: Monday, 30 August 2004 09:59 BST
Sunday, 29 August 2004


The Semantics of Imperatives within a Theory of Clause Types

by Paul Portner

Though individual clause types - especially declaratives, interrogatives, and imperatives - have been studied extensively, there is less work on clause type systems.1 This is so despite the fact that clause type systems have properties which suggest that they will prove revealing concerning the nature of Universal Grammar. For example, we may ask:

(1) a. Why are some clause types (declaratives, interrogatives, and
imperatives) universal?
b. Why are some clause types possible but not universal (e.g.,
exclamatives and promissives)?
c. Why are some intuitively plausible clause types in fact not attested, and perhaps not possible (e.g., "threatatives" and "warnatives")?

The contrast between imperatives and promissives brings out the issue well. These two types are functionally very similar: An imperative places a requirement on the addressee, while a promissive places a requirement on the speaker. Yet imperatives are apparently universal (and at least extremely common), while promissives are extremely rare. It does not seem easy to give a functional explanation for this contrast, and so in is reasonable to inquire into whether an explanation in terms of syntactic or semantic theory is possible. (...)

Source: The Semantics Archive


Posted by Tony Marmo at 08:30 BST
Updated: Monday, 30 August 2004 01:54 BST
Friday, 27 August 2004

Here is a new website for paraconsistency:

The home page for the philosophy of paraconsistency

Aim of this site

This site results, among others, from discussions between Jean-Yves Beziau and Alessio Moretti, about the philosophical relevance of paraconsistent logic. It's aim is to offer a frame to all searchers interested in exploring the philosophical implications of the many logical systems and approaches going under the general banner "paraconsistency". The analysis is, more or less, the following :
1) paraconsistent logic is by now a quite well established branch of mathematics, exploring mainly the properties of logical "negation". One has to note that the many technical results about paraconsistency are still quite unknown to the non-paraconsistent working mathematician, not to speak about the philosopher not used to mathematical formalisms.
2) Although paraconsistency was, at his beginning, motivated by deep philosophical reasons, it seems, by some kind of paradox, that now that the technical machinery has reached a satisfactory level of maturity, the philosophical interpretations of this new logical landscape are very few and still seem to lack of philosophical depth, at least in the sense of not (yet) reaching the scope of possible applications.
3) This unsatisfactory situation of the philosophical side of the enterprise is not due to some intrinsic reason of the subject, say "paraconsistency is not philosophically interesting". On the contrary, paraconsistency is highly interesting, probably crucial, to the philosopher (i.e. to all kinds of philosophers), and the relative poverty of the reflection thereupon is more a matter of coordination of the researchers and of accessibility, for the professional philosopher, of the technical discoveries, these being most of the time rather unintelligible to that respectable majority of philosophers not that much used to mathematical sophistication.
4) Which gives us the policy to follow for our present project : <...>


Posted by Tony Marmo at 01:01 BST
Updated: Monday, 30 August 2004 02:02 BST
Wednesday, 25 August 2004


An Expressive First-Order Logic with Flexible Typing for Natural Language Semantics

by Chris Fox and Shalom Lappin

We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. 1We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like most . We use the type system and our treatment of generalized quantifiers in natural language to construct a type-theoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous type-theoretic analyses of this phenomenon.


Posted by Tony Marmo at 09:07 BST
Updated: Wednesday, 25 August 2004 09:34 BST
Tuesday, 24 August 2004


Hempel's Raven Paradox: A Lacuna in the Standard Bayesian Solution

by Peter B. M. Vranas

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians.


Posted by Tony Marmo at 03:14 BST
Monday, 23 August 2004
The Fuzzy Logic Debate
Entemann (2002) [1] versus Pelletier(2004)[2]: a debate about what are the misconceptions about Fuzzy Logic.

The Fuzzy Logic Debate [1]

Fuzzy Logic: Misconceptions and Clarifications

by Carl W. Entemann

Some commonly accepted statements concerning the basic fuzzy logic proposed by Lotfi Zadeh in 1965, have led to suggestions that fuzzy logic is not a logic in the same sense as classical bivalent logic. Those considered herein are: fuzzy logic generates results that contradict classical logic, fuzzy logic collapses to classical logic, there can be no proof theory for fuzzy logic, fuzzy logic is inconsistent, fuzzy logic produces results that no human can accept, fuzzy logic is not proof-theoretic complete, fuzzy logic is too complex for practical use, and, finally, fuzzy logic is not needed. It is either proved or argued herein that all of the these statements are false and are, hence, misconceptions. A fuzzy logic with truth values specified as subintervals of the real unit interval [0.0, 1.0] is introduced. Proofs of the correctness, consistency, and proof theoretic completeness of the truth interval fuzzy logic are either summarized or cited. It is concluded that fuzzy logics deserve the accolade of logic to the same degree that the term applies to classical logics.

knowledge management, logic inference, logic processing, theorem proving, uncertainty, uncertainty reasoning

The Fuzzy Logic Debate [2]

On Some Alleged Misconceptions about Fuzzy Logic

by Francis Jeffry Pelletier

Entemann (2002) defends fuzzy logic by pointing to what he calls `misconceptions' concerning fuzzy logic. However, some of these `misconceptions' are in fact truths, and it is Entemann who has the misconceptions. The present article points to mistakes made by Entemann in three different areas. It closes with a discussion of what sort of general considerations it would take to motivate fuzzy logic.

Fuzzy Logic, Proof Theory, Truth Interval Tableaux

Posted by Tony Marmo at 05:44 BST
Updated: Monday, 23 August 2004 05:58 BST


Natural Language Semantics' TOP 3

Focus Below the Word Level
by Ron Artstein
The Interpretation of Traces
by Uli Sauerland
Crossover Situations
by Daniel Buring

Posted by Tony Marmo at 05:20 BST
Sunday, 22 August 2004

A Poor Concept Script

by Hartley Slater
Source: AJL

The formal structure of Frege's `concept script' has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the paper then goes on to indicate the lines on which formal logic--and also the lambda calculus and set theory--needs to be restructured, to remove the difficulties.

Throughout the study of what have come to be known as first-, second-, and higher-order languages, what has been primarily overlooked is that these languages are abstractions. Many well known paradoxes, we shall see, arose because of the elementary level of simplification which has been involved in the abstract languages studied. Straightforward resolutions of the paradoxes immediately appear merely through attention to languages of greater sophistication, notably natural language, of course. The basic problem has been exclusive attention to a theory in place of what it is a theory of, leading to a focus on mathematical manipulation, which `brackets off' any natural language reading.


Posted by Tony Marmo at 01:01 BST
Updated: Sunday, 22 August 2004 01:03 BST
Friday, 20 August 2004


Information State Update: Semantics or Pragmatics?

by Raquel Fern?ndez and Matthew Purver (2004)

We argue for an approach which treats the compositional semantic content of an utterance as including its basic dialogue update effects - those which can be derived entirely from its semantic and syntactic properties.

This allows us to capture the distinction between these integral semantic contextual effects and those pragmatic effects which can only be determined from the interaction between features of the utterance and the context itself.


Posted by Tony Marmo at 18:22 BST
Updated: Friday, 20 August 2004 18:24 BST

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