scholarly journals Unified correspondence and proof theory for strict implication

2016 ◽  
pp. exw012 ◽  
Author(s):  
Minghui Ma ◽  
Zhiguang Zhao
Keyword(s):  
Proof Theory ◽  
Strict Implication

Structural Proof Theory

2001 ◽  
Author(s):  
Sara Negri ◽  
Jan von Plato ◽  
Aarne Ranta
Keyword(s):  
Proof Theory ◽  
Structural Proof Theory

Basic Proof Theory

2000 ◽  
Author(s):  
A. S. Troelstra ◽  
H. Schwichtenberg
Keyword(s):  
Proof Theory

Proof Theory of the Cut Rule

2018 ◽  
Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely
Keyword(s):  
Proof Theory ◽  
Graphical Representation ◽  
Basic Component ◽  
Graphical Representations ◽  
Mathematical Language ◽  
Basic Logic ◽  
Cut Rule ◽  
Structural Rules ◽  
The One ◽  
Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science

1987 ◽  
Vol 10 (4) ◽  
pp. 387-413
Author(s):  
Irène Guessarian
Keyword(s):  
Logic Programming ◽  
Computer Science ◽  
Proof Theory ◽  
Algebraic Structures ◽  
Data Bases

This paper recalls some fixpoint theorems in ordered algebraic structures and surveys some ways in which these theorems are applied in computer science. We describe via examples three main types of applications: in semantics and proof theory, in logic programming and in deductive data bases.

Non-well-founded Proof Theory of Transitive Closure Logic

2020 ◽  
Vol 21 (4) ◽  
pp. 1-31
Author(s):  
Liron Cohen ◽  
Reuben N. S. Rowe
Keyword(s):  
Proof Theory ◽  
Transitive Closure

On the logic of incomplete answers

1965 ◽  
Vol 30 (1) ◽  
pp. 65-68 ◽  
Author(s):  
M. J. Cresswell
Keyword(s):  
Formal Analysis ◽  
Complete List ◽  
Strict Implication ◽  
Complete Answer ◽  
Questions And Answers ◽  
Image Position

I have argued in [1] that a concept bearing some resemblance to ‘p is the answer to d’ (p a proposition and d a question) can be defined wherever d has the form,‘For which a's is it the case that A (a)?’ (Qa)A(a)where a is a variable and A a wff containing a. To say that p is the true and complete answer to (Qa)A(a) is expressed as saying that p is logically equivalent to the true conjunction of A(a) or ~A(a) for each a. It is defined as;Such a concept of answer is like Belnap's [2] direct true answer to a complete list question, or like Harrah's use [3] (p. 43) of the notion of a state description. The main difference between my approach and that of Belnap and Harrah is that while they are concerned to develop a formal metalanguage for discussion of questions and answers I am concerned to express, as far as possible in existing systems, certain interrogative statements; in particular statements of the form ‘— is the (an) answer to —’.While the account in [1] does give a formal analysis of one ‘answer’ concept there are respects in which it is inadequate.1. Since it uses entailment (or strict implication) to define the relation between p the answer and d the question we can shew that if p is the answer to d and q is logically equivalent to p then q is the answer to d.

scholarly journals Dummetova koncepcija kao teorija značenja za Hintikkin tip semantike teorije igre (III)

2018 ◽  
Vol 30 (7) ◽  
Author(s):  
Heda Festini
Keyword(s):  
General Theory ◽  
Information Seeking ◽  
Proof Theory ◽  
Winning Strategy ◽  
General Information ◽  
Language Games ◽  
Inductive Probability ◽  
Theory Of Meaning ◽  
The Difference ◽  
Key Terms

With the analysis of the key terms such as truth/use, proof - verification, falsification, inductive probability/semantic probability, winning/losing, winning strategy, it is shown that Dummett’s general theory of meaning does not include Hintikka’s game theory, that it, the conception of the winning strategy. The difference between them arises from the different understanding of Wittgenstein's idea about language games and from their attitudes toward theoretical proof theory. Hintikka’s semantic games about exploration of the world do not reject the bivalence principle but he gives it a different characteristic - one of the two players always has a winning strategy. Looking at Dummett’s philosophical theory of meaning and the most recent Hintikka’s suggestion about general information - seeking through questioning and answering, the author establishes that Dummett’s falsificational and dialogical games as well as Hintikka’s semantic games are subparts of Hintikka’s general information - seeking game Thus Dummett’s statement that Hintikka’s semantic games can be subsumed under Dummett’s conception is rejected and thus the answer is partly given to Saarinen’s suggestion that new affinity should be established. Apart from the comparison of these views with the outline of possible Wittgenstein’s general theory of meaning as rule - testing, together with his treatment (although not always adequate) of verification/falsification, inductive probability and čonfirmation/corroboration, the advantage of Wittgenstein’s view is affirmed.

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