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We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…
A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed…
We present a hierarchical framework for analysing propositional linear-time temporal logic (PTL) to obtain standard results such as a small model property, decision procedures and axiomatic completeness. Both finite time and infinite time…
The definition of probabilities in eternally inflating universes requires a measure to regulate the infinite spacetime volume, and much of the current literature uses a global time cutoff for this purpose. Such measures have been found to…
We develop a timeout based extension of propositional linear temporal logic (which we call TLTL) to specify timing properties of timeout based models of real time systems. TLTL formulas explicitly refer to a running global clock together…
We study frequency linear-time temporal logic (fLTL) which extends the linear-time temporal logic (LTL) with a path operator $G^p$ expressing that on a path, certain formula holds with at least a given frequency p, thus relaxing the…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…
Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula f, which…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear…
Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…
Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk,…
This paper examines bilateral claims problems with lower and upper exclusion thresholds that determine whether an individual is excluded from initial gains or losses. We introduce the exclusion dilation operator, a method that transforms…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
This work presents the deductive system Double Propositional Logic, LD, along with the semantics of possible worlds that characterize it. LD includes an alternate affirmation operator and an alternate negation operator and is not valid for…