Inference in Probabilistic Logic Programs using Weighted CNF's

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for this formalism. The contribution of this paper is that we develop efficient inference algorithms for these tasks. This is based on a conversion of the probabilistic logic program and the query and evidence to a weighted CNF formula. This allows us to reduce the inference tasks to well-studied tasks such as weighted model counting. To solve such tasks, we employ state-of-the-art methods. We consider multiple methods for the conversion of the programs as well as for inference on the weighted CNF. The resulting approach is evaluated experimentally and shown to improve upon the state-of-the-art in probabilistic logic programming

Using Z3 to Verify Inferences in Fragments of Linear Logic

Linear logic is a substructural logic proposed as a refinement of classical and intuitionistic logics, with applications in programming languages, game semantics, and quantum physics. We present a template for Gentzen-style linear logic sequents that supports verification of logic inference rules using automatic theorem proving. Specifically, we use the Z3 Theorem Prover [8] to check targeted inference rules based on a set of inference rules that are presumed to be valid. To demonstrate the approach, we apply it to validate several derived inference rules for two different fragments of linear logic: MLL+Mix (Multiplicative Linear Logic extended with a Mix rule) and MILL (Multiplicative Intuitionistic Linear Logic).Comment: In Proceedings FROM 2023, arXiv:2309.1295

Solving Practical Reasoning Poblems with Extended Disjunctive Logic Programming

We present a definition of stable generated models for extended generalized logic programs (EGLP) which a) subsumes the definition of the answer set semantics for extended normal logic programs [GL91]; and b) does not refer to negation-as-failure by allowing for arbitrary quantifier free formulas in the body and in the head of as rule (i.e. does not depend on the presence of any specific connective, nor any specific syntax of rules). We show how to solve classical ATP problems in the framework of extended disjunctive logic programming (EDLP) where neither Contraposition nor the Law of the Excluded Middle are admitted principles of inference. Besides being able to solve classical ATP problems in a monotonic reasoning mode, EDLP can as well treat commonsense reasoning problems by employing its intrinsic nonmonotonic inference capabilities based on stable generated models. EDLP thus proves itself as a general-purpose AI reasoning system

Modal and Relevance Logics for Qualitative Spatial Reasoning

Qualitative Spatial Reasoning (QSR) is an alternative technique to represent spatial relations without using numbers. Regions and their relationships are used as qualitative terms. Mostly peer qualitative spatial reasonings has two aspect: (a) the first aspect is based on inclusion and it focuses on the ”part-of” relationship. This aspect is mathematically covered by mereology. (b) the second aspect focuses on topological nature, i.e., whether they are in ”contact” without having a common part. Mereotopology is a mathematical theory that covers these two aspects. The theoretical aspect of this thesis is to use classical propositional logic with non-classical relevance logic to obtain a logic capable of reasoning about Boolean algebras i.e., the mereological aspect of QSR. Then, we extended the logic further by adding modal logic operators in order to reason about topological contact i.e., the topological aspect of QSR. Thus, we name this logic Modal Relevance Logic (MRL). We have provided a natural deduction system for this logic by defining inference rules for the operators and constants used in our (MRL) logic and shown that our system is correct. Furthermore, we have used the functional programming language and interactive theorem prover Coq to implement the definitions and natural deduction rules in order to provide an interactive system for reasoning in the logic