We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO or GF (even the three-variable fragment thereof), and that they are decidable and 2ExpTime-co...

Interval temporal logics formalize reasoning about interval structures over (usually) linearly ordered domains, where time intervals are the primitive ontological entities and truth of formulae is defined relative to time intervals, rather than time instants. In this paper, we introduce and study Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities r...

Impulsive differential equations, which arise in biology, physics, population dynamics, economics, etc., are a basic tool to study evolution processes that are subjected to abrupt in their states (see [8-12]). Recently, the existence results were extended to anti-periodic boundary value problems for first-order impulsive differential equations [13,14]. Very recently, Wang and Shen [15] investig...

FALL 1999 T TITLE of this article is also the title of a remarkable new book written by Liping Ma. The basic format of the book is simple. Each of the first four chapters opens with a standard topic in elementary school mathematics, presented as a part of a situation that would arise naturally in a classroom. These scenarios are followed by extensive discussion by teachers regarding how they wo...

personal identity is a problem in the possibility of resurrection. what criterion is there that we can say a resurrected man is the same as the expired one? what is the answer in dualism, and what is in physicalism? does this question cause to deny possibility of resurrection? some philosopher claim that we have no criterion for identity between these two. and then, they conclude that after lif...

Uniform one-dimensional fragment UF=1 is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified formula. The fragment is closed under Boolean operations, but additional restrictions (called uniformity conditions) apply to combinations of atomic formulas ...

In [5], van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretic argument, which provides no apparent bounds on the complexity of a decision procedure. We provide a syntactic argument that yields a procedure that is primitive recursive, although not el...

We present methods to answer to basic questions that arise when benchmarking optimization algorithms. The first one is: which algorithm is the ‘best’ one? and the second one: which algorithm should I use for my real world problem? Both are connected and neither is easy to answer. We present methods which can be used to analyse the raw data of a benchmark experiment and derive some insight regar...

Adults appear to be more sensitive to configural information, including second-order relations (the spacing of features), in faces than in other objects. Superior processing of second-order relations in faces may arise from our experience of identifying faces at the individual level of categorisation (eg Bob versus John) but other objects at the basic level of categorisation (eg table versus ch...