Related papers: Operators in the mind: Jan Lukasiewicz and Polish …
Developing neural architectures that are capable of logical reasoning has become increasingly important for a wide range of applications (e.g., natural language processing). Towards this grand objective, we propose a symbolic reasoning…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
We initiate a deep study of {\em Riesz MV-algebras} which are MV-algebras endowed with a scalar multiplication with scalars from $[0,1]$. Extending Mundici's equivalence between MV-algebras and $\ell$-groups, we prove that Riesz MV-algebras…
We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and…
The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which…
We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…
In this paper we give a new proof for the completeness of infinite valued propositional \L ukasiewicz logic introduced by \L ukasiewicz and Tarski in 1930. Our approach employs a Hilbert-style proof that relies on the concept of maximal…
Hypersequent calculus G{\L}$\forall$ for first-order {\L}ukasiewicz logic was first introduced by Baaz and Metcalfe, along with a proof of its approximate completeness with respect to standard $[0,1]$-semantics. The completeness result was…
The choice of activation functions and their motivation is a long-standing issue within the neural network community. Neuronal representations within artificial neural networks are commonly understood as logits, representing the log-odds…
We face the problems of correctness, optimality and precision for the static analysis of logic programs, using the theory of abstract interpretation. We propose a framework with a denotational, goal-dependent semantics equipped with two…
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Continuing to pursue a research direction that we already explored in connection with G\"odel-Dummett logic and Ruspini partitions, we show here that {\L}ukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy…
Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
The study discusses modeling diachronic processes by logistic regression. The phenomenon of nonlinear changes in language was first observed by Raimund Piotrowski (hence labelled as Piotrowski's law), even if actual linguistic evidence…