Search results for " Logic"
showing 10 items of 1720 documents
Weakly algebraizable logics
2000
AbstractIn the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.
Unification in superintuitionistic predicate logics and its applications
2018
AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) structural completeness, etc. For this aim we apply modified specific notions, introduced in proposition…
Basic Measure Theory
2020
In this chapter, we lay the measure theoretic foundations of probability theory. We introduce the classes of sets (semirings, rings, algebras, σ-algebras) that allow for a systematic treatment of events and random observations. Using the measure extension theorem, we construct measures, in particular probability measures on σ-algebras. Finally, we define random variables as measurable maps and study the σ-algebras generated by certain maps.
Nonlocalization Properties of Time Operators Transformations
2014
It is presented a general approach to the problem of extension of time operators and the associated Lambda transformations on singular measures. It is also shown that Lambda transformations defined on function spaces having the Urysohn property are non localized. Particular attention has been devoted to time and Lambda operators associated with the Walsh-Paley system and to a characterization of their domain and non locality.
Elementary Action Systems
2015
This chapter expounds basic notions. An elementary action system is a triple consisting of the set of states, the transition relation between states, and a family of binary relations defined on the set of states. The elements of this family are called atomic actions. Each pair of states belonging to an atomic action is a possible performance of this action. This purely extensional understanding of atomic actions is close to dynamic logic. Compound actions are defined as sets of finite sequences of atomic actions. Thus compound actions are regarded as languages over the alphabet whose elements are atomic actions. This chapter is concerned with the problem of performability of actions and the…
Unification in first-order transitive modal logic
2019
We introduce unification in first-order transitive modal logics, i.e. logics extending Q–K4, and apply it to solve some problems such as admissibility of rules. Unifiable formulas in some extensions of Q–K4 are characterized and an explicit basis for the passive rules (those with non-unifiable premises) is provided. Both unifiability and passive rules depend on the number of logical constants in the logic; we focus on extensions of Q–K4 with at most four constants ⊤,⊥,□⊥,◊⊤. Projective formulas, defined in a way similar to propositional logic, are used to solve some questions concerning the disjunction and existence properties. A partial characterization of first-order modal logics with pr…
Lawvere–Tierney sheaves in Algebraic Set Theory
2009
We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.
An environment based approach for the ant colony convergence
2020
Abstract Ant colony optimization (ACO) algorithms are a bio inspired solutions which have been very successful in combinatorial problem solving, also known as NP-hard problems, including transportation system optimization. As opposed to exact methods, which could give the best results of a tested problem, this meta-heuristics is based on the stochastic logic but not on theoretical mathematics demonstration (or only on certain well defined applications). According to this, the weak point of this meta-heuristics is his convergence, its termination condition. We can finds many different termination criteria in the scientific literature, yet most of them are costly in resources and unsuitable f…
Free Action and Interventionist Theory of Causality
2019
Intendo discutere il rapporto tra la teoria interventista della causalità e l’azione libera. Gli approcci interventisti alla causalità definiscono la causazione sulla base dell’“intervento”. Queste teorie possono essere riduttive, se spiegano le cause in base all’intervento umano come libero intervento umano, oppure non-riduttive, se considerano cause e interventi come due concetti inter-definiti, dove gli interventi sono considerati come esplicitamente non umani. Intendo mostrare che il dilemma tra teorie interventista della causalità di tipo riduttivo e non-riduttivo può essere superato in favore degli approcci riduttivi, con riferimento a ciò che la causazione è in senso antropologico e …
Dimension estimates for the boundary of planar Sobolev extension domains
2020
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.