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The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
We present a functional programming language for specifying constraints over tree-shaped data. The language allows for Haskell-like algebraic data types and pattern matching. Our constraint compiler CO4 translates these programs into…
We develop a qualitative model of decision making with two aims: to describe how people make simple decisions and to enable computer programs to do the same. Current approaches based on Planning or Decisions Theory either ignore uncertainty…
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the…
In safety-critical applications, guaranteeing the satisfaction of constraints over continuous environments is crucial, e.g., an autonomous agent should never crash into obstacles or go off-road. Neural models struggle in the presence of…
We propose algebraic protocols that enable the definition of protocol templates and session types analogous to the definition of domain-specific types with algebraic datatypes. Parameterized algebraic protocols subsume all regular as well…
We study a propositional variant of Hoare logic that can be used for reasoning about programs that exhibit both angelic and demonic nondeterminism. We work in an uninterpreted setting, where the meaning of the atomic actions is specified…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced…
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…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logico-algebraic objects. As a result, the logic of experimental…
The intention of the present study is to establish general framework for automated problem solving by approaching the task universal algebraically introducing knowledge as realizations of generalized free algebra based nets, graphs with…
We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…