This paper presents an initial attempt at a solution to a challenge set by Prof. Henri Habrias to compare the questions raised by di erent methods in the formalization of an informal set of requirements. The notation used is Z, based on set theory and predicate logic, augmented with the schema notation for structuring. The original English language description of what is required is included ve...

The merits of representing scientific theories in formal logic are well-known. Expressing a scientific theory in formal logic explicates the theory as a whole, and the logic provides formal criteria for evaluating the theory, such as soundness and consistency. On the one hand, these criteria correspond to natural questions to be asked about the theory: is the theory contradiction-free? (is the ...

We present new preservation theorems that semantically characterize the ∃∀ and ∀∃ prefix classes of first order logic, for each natural number k. Unlike preservation theorems in the literature that characterize the ∃∗∀∗ and ∀∗∃∗ prefix classes, our theorems relate the count of quantifiers in the leading block of the quantifier prefix to natural quantitative properties of the models. As special ...

This paper analyzes the probabilistic description logic PSHIQ by looking at it as a fragment of probabilistic first-order logic with semantics based on possible worlds. We argue that this is an appropriate way of investigating its properties and developing extensions. We show how the previously made arguments about different types of first-order probabilistic semantics apply to P-SHIQ. This app...

The state-of-the-art definitions of actual cause by Pearl and Halpern suffer from the modest expressivity of causal models. We develop a new definition of actual cause in the context of situation calculus (SC) basic action theories. As a result, we avoid the paradoxes that arise in causal models and can identify complex actual causes of conditions expressed in first-order logic. We provide a fo...

We review some results on global and local temporal logic on Mazurkiewicz traces. Our main contribution is to show how to derive the expressive completeness of global temporal logic with respect to first order logic [9] from the similar result on local temporal logic [11].

This paper contains an extended and improved version of the description of the FDMM formalism presented at ICEIS’2012. FDMM is a formalism to describe how meta models and models are defined in the ADOxx approach as used in the Open Models Initiative. It is based on set theory and first order logic statements. In this way, an exact description of ADOxx meta models and corresponding models can be...

Bayesian logic provides a rational model of probability judgments deviating from the standard extensional norm of extensional probability. It formalizes the general idea of an inductive pattern logic that may resolve paradoxes of inclusion. Bayesian logic predicts that it should be possible to generalize the phenomenon of frequency-based logical conjunction fallacies to a system of logical incl...

James Allen and Pat Hayes have considered axioms expressed in first-order logic for relations between time intervals [AllHay85, AllHay87.1, AllHay87.2]. One important consequence of the results in this paper is that their theory is decidable [Lad87.4]. In this paper, we characterise all the models of the theory, and of an important subtheory. A model is isomorphic to an interval structure INT(S...

Predicate construction is a guided search process: a space of predicates must be enumerated in some systematic way in order to find, according to some criterion, a suitable predicate for some purpose. Often the search space is large and heuristics are used to guide the search. Typically, predicate construction is studied and implemented in the context of first-order logic. In this paper, I outl...