The Loop Latest Issue
Ideas for curious minds.
Algebrica offers a unique experience with a thoughtfully curated selection of high-quality content that is truly worth exploring.
Antonio Lupetti

Artificial intelligence systems rely on complex automated deduction algorithms that originate from the formalism of logic. There are various types of logics, such as propositional logic, predicate logic, and descriptive logic. In this post, I will briefly explain the characteristics of propositional logic and how it is used to determine the truth values of propositional formulas. Propositional logic studies inferential relationships among sentences, focusing on logical operators called propositional connectives \( \neg \), \( \wedge \), \( \lor \), \( \rightarrow \), \( \leftrightarrow \), \( \oplus \).

Antonio Lupetti

This week’s issue of The Loop delves deeply into the recurrent argument regarding the concerns over emerging technologies and their impact on society. It’s fascinating to note that this debate is not a new phenomenon. In the modern era, it has been a part of our societal discourse since the 1950s, as highlighted by Isaac Asimov in his writings:

Whenever man develops a new and powerful technology, he inevitably worries about the potential negative consequences.

Isaac Asimov, The Naked Sun (1956)

The introduction of personal computers in the 1980s sparked similar discussions, and today, we revisit these concerns with the emergence of artificial intelligence.

Antonio Lupetti

When dealing with a large amount of text, it is essential to have tools that can help computers recognize and evaluate the similarity between documents. One of the most effective methods in this field is cosine similarity. This transformative approach allows for the semantic interpretation of human language in a format that machines can easily understand.

The cosine similarity between two vectors is calculated using the following formula:

\[ \text{cosine similarity} \ (V_x, V_y) = \frac{\sum_{i=1}^{n} V_{x_i} \cdot V_{y_i}}{\sqrt{\sum_{i=1}^{n} (V_{x_i})^2} \times \sqrt{\sum_{i=1}^{n} (V_{y_i})^2}} \]

or in compact form:

\[\text{cosine similarity} \ (V_x, V_y) = \frac{V_x \cdot V_y}{||V_x|| \ ||V_y||}\]

In this post, I propose a practical example of how to assess the similarity between different documents by referencing some simple cases.

Antonio Lupetti


How Machine Think — Artificial intelligence merges methods to replicate human thought, driven by computing power, vast data, and advanced algorithms. Its rapid advancement transforms sectors and reshapes society by enhancing problem-solving capabilities through symbolic processing, knowledge representation, and logical inference.

Artificial intelligence is a field that combines different methods and approaches to imitate human thought processes, which a computerized system can replicate. The rapid progress we have observed in recent years in this field is driven by the growing computing power, the abundance of extensive datasets, and the ongoing research and development of advanced algorithms.

Read more