Logic Journal of IGPL - current issue

Logics with the Qualitative Probability Operator

Ognjanovic, Z., Perovic, A., Raskovic, M. — 2008-03-17

The paper presents several strongly complete axiomatizations of qualitative probability within the framework of probabilistic logic. We show that in the proposed semantics qualitative probabilities are characterized by probability functions, so they also are comparative probabilities.

Heterogeneous Fibring of Deductive Systems Via Abstract Proof Systems

Cruz-Filipe, L., Sernadas, A., Sernadas, C. — 2008-03-17

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way (e.g via Hilbert calculi). Heterogeneous fibring, allowing the original logics to have different presentations (e.g. one presented by a Hilbert calculus and the other by a sequent calculus), has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated.

Sequent Calculi for Some Strict Implication Logics

Ishigaki, R., Kashima, R. — 2008-03-17

We introduce various sequent systems for propositional logics having strict implication, and prove the completeness theorems and the finite model properties of these systems.The cut-elimination theorems or the (modified) subformula properties are proved semantically.

Constructing Finite Least Kripke Models for Positive Logic Programs in Serial Regular Grammar Logics

Nguyen, L. A. — 2008-03-17

A serial context-free grammar logic is a normal multimodal logic L characterized by the seriality axioms and a set of inclusion axioms of the form _t->_s₁..._{s_k}. Such an inclusion axiom corresponds to the grammar rule t -> s₁... s_k. Thus the inclusion axioms of L capture a context-free grammar $$\mathcal{G}(L)$$. If for every modal index t, the set of words derivable from t using $$\mathcal{G}(L)$$ is a regular language, then L is a serial regular grammar logic.

In this paper, we present an algorithm that, given a positive multimodal logic program P and a set of finite automata specifying a serial regular grammar logic L, constructs a finite least L-model of P. (A model M is less than or equal to model M' if for every positive formula , if M then M' .) A least L-model M of P has the property that for every positive formula , P iff M . The algorithm runs in exponential time and returns a model with size 2^O(n³). We give examples of P and L, for both of the case when L is fixed or P is fixed, such that every finite least L-model of P must have size 2⁽ⁿ⁾. We also prove that if G is a context-free grammar and L is the serial grammar logic corresponding to G then there exists a finite least L-model of _s p iff the set of words derivable from s using G is a regular language.

On Ignorance and Contradiction Considered as Truth-Values

Dubois, D. — 2008-03-17

A critical view of the alleged significance of Belnap four-valued logic for reasoning under inconsistent and incomplete information is provided. The difficulty lies in the confusion between truth-values and information states, when reasoning about Boolean propositions. So our critique is along the lines of previous debates on the relevance of many-valued logics and especially of the extension of the Boolean truth-tables to more than two values as a tool for reasoning about uncertainty. The critique also questions the significance of partial logic.

Conferences

2008-03-17

Acknowledgements

2008-03-17