characteristica

Relative Identity: https://plato.stanford.edu/entries/identity-relative/

Even if there is something to the thought that inquiry aims at truth, it has to be admitted that truth is a rather coarse-grained property of propositions. Some falsehoods seem to realize the aim of getting at the truth better than others. Some truths better realize the aim than other truths. And perhaps some falsehoods even realize the aim better than some truths do. The dichotomy of the class of propositions into truths and falsehoods needs to be supplemented with a more fine-grained ordering — one which classifies propositions according to their closeness to the truth, their degree of truthlikeness, or their verisimilitude.

A formal theory of truth, alternative to Tarski's “orthodox” theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and “paradoxical” sentences

• An introduction: http://fitelson.org/probability/haack_truth.pdf • Deflationary theory of truth: https://plato.stanford.edu/entries/truth-deflationary/ • Corrispondence theory of truth:https://plato.stanford.edu/entries/truth-correspondence/ • Coherence theory of truth: https://plato.stanford.edu/entries/truth-coherence/ • Pragmatist theories of truth: https://plato.stanford.edu/entries/pragmatism/#PraTheTru • Identity theory of truth: https://plato.stanford.edu/entries/truth-identity/

«An axiomatic theory of truth is a deductive theory of truth as a primitive undefined predicate. Because of the liar and other paradoxes, the axioms and rules have to be chosen carefully in order to avoid inconsistency. Many axiom systems for the truth predicate have been discussed in the literature and their respective properties been analysed. Several philosophers, including Donald Davidson and many deflationists, have endorsed axiomatic theories of truth in their accounts of truth. The logical properties of the formal theories are relevant to various philosophical questions, such as questions about the ontological status of properties, Gödel's theorems, truth-theoretic deflationism, eliminability of semantic notions and the theory of meaning»

a. Truth should be expressed by a predicate (and a theory of syntax should be available) b. If a theory of truth is added to mathematical or empirical theories, it should be possible to prove the latter true c. The truth predicate should not be subject to any type restrictions d. T-biconditionals should be derivable unrestrictedly e. Truth should be compositional f. The theory should allow for standard interpretations g. The outer logic and the inner logic should coincide h. The outer logic should be classical

«The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective». Non-normal modal logics: a challenge to proof theory by Sara Negri  «A general procedure that follows the guidelines of inferentialism is presented for generating G3-style sequent calculi for non-normal modal logics on the basis of neighbourhood semantics» 

«I formulate a Gentzen consecution calculus for an indefinite number of logics all mixed together, including boolean (two valued), intuitionistic, relevance, and (various) modal logics. This is accomplished by augmenting and refining the structural ideas of Gentzen (1934). The key feature of the calculus permitting control in the presence of multiple logics is this: every "positive part" of a consecution can he displayed as the consequent, standing alone, of an equivalent consecution; and every "negative part" can be displayed as the antecedent, standing alone, of an equivalent consecution; such a calculus I call a "Display logic"». 

Generalised proof-theory for multi-agent autoepistemic reasoning By Yamguth Permpoontanalarp «Over the past few years, several different approaches have been proposed to deal with multi- agent autoepistemic reasoning. Despite some limitations, each approach is important in its own right. While Pafikh’s approach allows an agent to reason uonmonotonically about other agents’ knowledge, it cannot reason about other agents’ nonmonotonic reasoning. Morgensteru’s logic provides a limited way to deal with the problem but unfortunately it is not constructive. Although Halperu introduces an alsorithmic definition of multi-agent nonmonotonic reasoning, his approach cannot deal with default reasoning even for the single-agent case. The purpose of this paper is to propose an integrated theory that deals with these problems. Using examples from speech acts theory, we demonstrate some unintnitive results against existing approaches. We then develop a simple and yet generalised proof-theoretic framework with constructive interpretation for multi-agent autoepistemic reasoning. We show that this framework retains the advantages of existing approaches but does not have their peculiar results». All They Know : A Study in Multi-Agent Autoepistemic Reasoning  by Gerhard Lakemeyer « With few exceptions the study of nonmonotonic reasoning has been confined to the single-agent case. However, it has been recognized that intelligent agents often need to reason about other agents and their ability to reason nonmonotonically. In this paper we present a formalization of multi-agent autoepistemic reasoning. In particular, we propose an n-agent modal belief logic, which allows us to express that a formula (or finite set of them) is all an agent knows, which may include beliefs about what other agents believe. The paper presents a formal semantics of the logic in the possible world framework. We provide an axiomatization, which is complete for a large fragment of the logic and sufficient to characterize interesting forms of multi-agent autoepistemic reasoning. We also extend the stable set and stable expansion ideas of single-agent autoepistemic logic to the multi-agent case». 

​«This entry concentrates on the emergence of non-trivial logical themes and notions from the discussion on paradoxes from the beginning of the 20th century until 1945, and attempts to assess their importance for the development of contemporary logic».

«The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory»

Ambi∈nt Some good music to listen to ;)

Sentences like ‘4 is even’ are not true (indeed, they're not true for the reason that fictionalists give, and so it follows that fictionalism is true).

According to the Heyting–Brower–Kolmogorov interpretation, a proof of A → B is a construction which permits us to transform any proof of A into a proof of B. Curry-Howard isomorphism takes seriously this interpretation, and gives syntactic representations of such construction. «The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed λ-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc»

«The Open Logic Project is a collection of teaching materials on mathematical logic aimed at a non-mathematical audience, intended for use in advanced logic courses as taught in many philosophy departments. It is open-source: you can download the LaTeX code. It is open: you’re free to change it whichever way you like, and share your changes. It is collaborative: a team of people is working on it, using the GitHub platform, and we welcome contributions and feedback. And it is written with configurability in mind» Moreover, Open Logic Project’s team has commissioned Matthew Leadbeater, a Calgary illustrator, to draw some fantastic line art portraits of logicians. It is possible to take a look at the portraits and download them here:  http://openlogicproject.org/2016/08/25/line-art-portraits-of-logicians/ Matthew Leadbeater personal website: http://www.mattleadbeater.com/

http://www.cs.ru.nl/~henk/ https://barendregtlogicpapers.wordpress.com/logic-publications/ http://www.cs.ru.nl/~henk/tm2.pdf http://cs.ru.nl/~henk/G.pdf

«We generally take agents who fall short of the demands of logic to be rationally defective. This suggests that logic has a normative role to play in our rational economy; it instructs us how we ought or ought not to think or reason. The notion that logic has such a normative role to play is deeply anchored in the way we traditionally think about and teach logic. [...]  This entry is concerned with the question as to whether the tradition and the intuitions that appear to underwrite it are correct. In other words, it is concerned with the question as to whether logic has normative authority over us? And if so, in what sense exactly it can be said to do so?»