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Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…
We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a simple system relying on the involutive status of negation. The second one…
We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The…
Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
In a previously published ENTCS paper (Santos et al. (2016)), we introduced a sequent calculus called $\mathbf{LMT^{\rightarrow}}$ for Minimal Implicational Propositional Logic ($\mathbf{LMT^{\rightarrow}}$). This calculus provides a proof…
A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
Action languages have emerged as an important field of Knowledge Representation for reasoning about change and causality in dynamic domains. This article presents Cerbere, a production system designed to perform online causal, temporal and…
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…
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…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
An approach to clustering is presented that adapts the basic top-down induction of decision trees method towards clustering. To this aim, it employs the principles of instance based learning. The resulting methodology is implemented in the…
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
We investigate the cyclic proof theory of extensions of Peano Arithmetic by (finitely iterated) inductive definitions. Such theories are essential to proof theoretic analyses of certain `impredicative' theories; moreover, our cyclic systems…
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem…