Related papers: On Measure Quantifiers in First-Order Arithmetic (…
We take the view that physical quantities are values generated by processes in measurement, not pre-existent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into…
A first-order logic with quantum variables is needed as an assertion language for specifying and reasoning about various properties (e.g. correctness) of quantum programs. Surprisingly, such a logic is missing in the literature, and the…
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L_1 is more succinct than another logic L_2 if all properties that can be expressed in L_2 can be expressed in L_1 by formulas of…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…
The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…