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#### Identity, Equality, Nameability and Completeness

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the ...

#### Bayesian Propositional Logic

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w , where w is a probability function on a Boolean ...

#### An Inferentially Many-Valued Two-Dimensional Notion of Entailment

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely ...

#### Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] ...

#### On Theses without Iterated Modalities of Modal Logics Between C1 and S5. Part 2

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

This is the second, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only ...

#### A Syntactic Approach to Closure Operation

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

In the paper, tracing the traditional Hilbert-style syntactic account of logics, a syntactic characteristic of a closure operation defined on a complete lattice follows. The approach is based on observation that the role ...

#### Deontic Paradoxes and Tableau System for Kalinowski’s Deontic Logic K1

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau ...

#### Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical ...

#### Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the ...

#### Cut Elimination Theorem for Non-Commutative Hypersequent Calculus

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

Hypersequent calculi (HC) can formalize various non-classical logics. In [9] we presented a non-commutative variant of HC for the weakest temporal logic of linear frames Kt4.3 and some its extensions for dense and serial ...