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## The relative consistency of system RRC* and some of its extensions

### Studia Logica (1994-09-01) 53: 351-360 , September 01, 1994

We present a relative consistency proof for second order system*RRC** and for certain important extensions of this system. The proof proceeds as follows: we prove first the equiconsistency of the strongest of such extensions (viz., system*H RRC**+(∃/*CP***)) with second order system*T*_{λ}^{*}
. Now, N. Cocchiarella has shown that*T*_{λ}^{*}
is relatively consistent to system*T**+*Ext*; clearly, it follows that*H RRC**+(∃/*CP***) is relatively consistent to*T*+E*_{xt}. As an immediate consequence, the relative consistency of*RRC** and the other extensions also follows, being all of them subsystems of*H RRC**+(∃/*CP***).

## Indukcja enumeracyjna a teoria gier

### Studia Logica (1960-12-01) 10: 37 , December 01, 1960

## Bi-Simulating in Bi-Intuitionistic Logic

### Studia Logica (2016-10-01) 104: 1037-1050 , October 01, 2016

Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindström and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated models nor elementary chains.

## P1 algebras

### Studia Logica (1994-03-01) 53: 21-28 , March 01, 1994

In [3] the authors proved that the deductive system*P1* introduced by Sette in [6] is algebraizable. In this paper we study the main features of the class of algebras thus obtained. The main results are a complete description of the free algebras in*n* generators and that this is not a congruence modular quasi-variety.

## Ewa Orlowska and Joanna Golinska-Pilarek, Dual Tableaux: Foundations, Methodology, Case Studies, Springer, Series: Trends in Logic, Vol. 33, 2011, pp. xvi+523, 113 illus. ISBN: 978-94-007-0004-8 (hardcover) EURO 181,85, 978-94-007-0005-5 (eBook) EURO 159,99.

### Studia Logica (2013-02-01) 101: 229-232 , February 01, 2013

## The converse principal type-scheme theorem in lambda calculus

### Studia Logica (1992-03-01) 51: 83-95 , March 01, 1992

A principal type-scheme of a λ-term is the most general type-scheme for the term. The converse principal type-scheme theorem (J.R. Hindley, *The principal typescheme of an object in combinatory logic, Trans. Amer. Math. Soc.**146* (*1969) 29–60*) states that every type-scheme of a combinatory term is a principal type-scheme of some combinatory term.

This paper shows a simple proof for the theorem in λ-calculus, by constructing an algorithm which transforms a type assignment to a λ-term into a principal type assignment to another λ-term that has the type as its principal type-scheme. The clearness of the algorithm is due to the characterization theorem of principal type-assignment figures. The algorithm is applicable to BCIW-λ-terms as well. Thus a uniform proof is presented for the converse principal type-scheme theorem for general λ-terms and BCIW-λ-terms.

## Negative Equivalence of Extensions of Minimal Logic

### Studia Logica (2004-12-01) 78: 417-442 , December 01, 2004

Two logics *L*_{1} and *L*_{2} are negatively equivalent if for any set of formulas *X* and any negated formula ¬ϕ, ¬ϕ can be deduced from the set of hypotheses *X* in *L*_{1} if and only if it can be done in *L*_{2}. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.

## Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory

### Studia Logica (2010-03-01) 94: 245-269 , March 01, 2010

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz *n*-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the *n*-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz *n*-valued logic with truth constants, which generalizes Jónsson-Tarski duality for modal algebras to the *n*-valued case via fuzzy topology. We emphasize that fuzzy topological spaces naturally arise as spectrums of algebras of many-valued logics.

## Impugning Randomness, Convincingly

### Studia Logica (2012-04-01) 100: 193-222 , April 01, 2012

John organized a state lottery and his wife won the main prize. You may feel that the event of her winning wasn’t particularly random, but how would you argue that in a fair court of law? Traditional probability theory does not even have the notion of random events. Algorithmic information theory does, but it is not applicable to real-world scenarios like the lottery one. We attempt to rectify that.

## Negative Translations Not Intuitionistically Equivalent to the Usual Ones

### Studia Logica (2013-02-01) 101: 45-63 , February 01, 2013

We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.