Abstract In this paper, the theory of McCarthy’s extensional arrays enriched with a maxdiff operation (this returns biggest index where two given differ) is proposed. It known from literature that diff required for in order to enjoy Craig interpolation property at quantifier-free level. However, introduced merely instrumental purpose and has only purely formal meaning (it obtained Skolemization...

We introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant α ≥ 0 such that the "bargaining power" of a group is proportional to cα, where c is the cardinality of the group. Subject classification: JEL C71, C78

In an important paper, Amrita Dhillon [3] provided a multi-profile version of Harsanyi’s [5] single-profile theorem on utilitarianism. Like Harsanyi, she assumed that the social alternatives are lotteries. Individuals’ preferences satisfy the von Neumann-Morgenstern (vN-M) axioms, and have thus an expected utility representation. A social welfare function maps profiles of individuals’ preferenc...

As more complex applications are developed in Description Logics (DL), providing explanation services for DL reasoners becomes more crucial. We propose to use resolution proofs to construct explanations for unsatisfiability and inconsistency problems. Our approach is based on the observation that compared to natural deduction proofs, resolution technique is more focused, as all the literals inv...

Axiom pinpointing is the task of identifying the axioms that are responsible for a consequence. It is a fundamental step for tasks like ontology revision and context-based reasoning, among many others. One known approach is to reduce axiom pinpointing to an enumeration problem over a set of Horn clauses. We introduce the new SATPin system, which combines techniques from axiom pinpointing and mi...

We present a logic for the reasoning about necessity and justifications which is independent from relational semantics. We choose the concept of justification – coming from a class of Justification Logics (Artemov 2008, Fitting 2009) – as the primitive notion on which the concept of necessity is based. Our axiomatization extends Suszko’s non-Fregean logic SCI (Brown, Suszko 1972) by basic axiom...

This tutorial deals with the application of the Axiom of Choice in one of its popular disguises to objects which are of some interest in computer science (like lattices, Boolean algebras, filters and ideals, games). We discuss some common variants of this axiom such as Zorn's Lemma, Tuckey's Maximality Principle, the Well-Ordering Theorem and the Maximal Ideal Theorem; each equivalence gives ap...

An arithmetically complete axiom system for full Algol-like higher order procedures with mode depth one is presented. To show soundness, a translation of the calculus into a variant of Dynamic Logic is deened. The completeness proof is outlined.