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Senza richiedere prerequisiti il testo si propone di fornire una dimostrazione dei fondamentali teoremi della logica matematica (compattezza, completezza di Gödel, Löwenheim-Skolem) introducendo i concetti sintattici e semantici in modo progressivo, dalla logica booleana a quella predicativa. Per facilitare la lettura attiva, il testo contiene numerosi esercizi.

Algebra, Boolean. --- Logic, Symbolic and mathematical. --- Logic. --- Mathematics -- Philosophy. --- Mathematics. --- Predicate (Logic). --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Predicate (Logic) --- Boolean algebra --- Boole's algebra --- Predicables (Logic) --- Predication (Logic) --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Mathematical logic. --- Semantics. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Algebraic logic --- Set theory --- Categories (Philosophy) --- Language and logic --- Logic --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- Computer science. --- Formal semantics --- Semasiology --- Semiology (Semantics) --- Comparative linguistics --- Information theory --- Language and languages --- Lexicology --- Meaning (Psychology) --- Informatics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism

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In order to solve real-world tasks, intelligent machines need to be able to act in noisy worlds where the number of objects and the number of relations among the objects varies from domain to domain. Algorithms that address this setting fall into the subfield of artificial intelligence known as statistical relational artificial intelligence (StaR-AI).While early artificial intelligence systems allowed for expressive relational representations and logical reasoning, they were unable to deal with uncertainty. On the other hand, traditional probabilistic reasoning and machine learning systems can capture the inherent uncertainty in the world, but employ a purely propositional representation and are unable to capture the rich, structured nature of many real-world domains.StaR-AI encompasses many strains of research within artificial intelligence. One such direction is statistical relational learning which wants to unify relational and statistical learning techniques. However, only a few of these techniques support decision making processes.This thesis advances the state-of-the-art in statistical relational learning by making three important contributions. The first contribution is the introduction of a novel representation, called causal probabilistic time-logic (CPT-L) for stochastic relational processes. These are stochastic processes defined over relational state- spaces and they occupy an intermediate position in the expressiveness/efficiency trade-off. By focusing on the sequential aspect and deliberately avoiding the complications that arise when dealing with hidden states, the algorithms for inference and learning for CPT-L are more efficient than those of general purpose statistical relational learning approaches. The second contribution is that we show how to adapt and generalize the algorithms developed for CPT-L so that they can be used to perform parameter estimation in the probabilistic logic programming language ProbLog. The final contribution of this thesis is a decision theoretic extension of the ProbLog language that allows to represent and to solve decision problems.

681.3*I23 <043> --- 681.3*I24 <043> --- 681.3*I26 <043> --- 681.3 <043> --- 681.3*I26 <043> Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32}--Dissertaties --- Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32}--Dissertaties --- 681.3*I23 <043> Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence)--Dissertaties --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence)--Dissertaties --- Knowledge representation formalisms and methods: frames and scripts; predicate logic; relation systems; representation languages; procedural and rule-based representations; semantic networks (Artificial intelligence)--Dissertaties --- Computer science--Dissertaties --- Theses