Carolina Ruiz

Theses and Ph.D. Dissertation

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Ph.D. in Computer Science. Dissertation
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"Semantics of Knowledge Based Systems with Multiple Forms of Negation"
In my Ph.D. thesis I introduced and investigated formalisms that admit several forms of default negation which interact with each other and with classical (or "explicit") negation in the same knowledge based system. Some theoretical aspects of this research include the investigation of the expressive power of the new formalisms and the characterization of their semantics. Practical issues include implementing procedures to compute in these formalisms, calculating the computational complexity of different reasoning tasks under the proposed semantics and modeling real life applications. One example is the problem of merging several knowledge bases, each of which uses a different rule for negation, and finding answers to queries in the combined knowledge base.

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M.S. in Computer Science. Thesis
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Formal Verification of Abstract Data Types and Code Synthesis.
Designed and developed an environment for the definition and manipulation of Abstract Data Types (ADTs), which provides a code synthesizer that automatically generates code in LISP and/or C which structurally and functionally implements an ADT. This code may be used in common applications. The environment includes also a theorem prover oriented to perform formal verification of ADTs as well as proving abstract properties of ADTs. It uses rewriting rules to produce and deal with canonical forms of ADT expressions.

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B.S. in Mathematics. Undergraduate Thesis
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Categorical Logic.
Showed that the category Dyn($\Sigma$) of automata and dynamorphisms over an alphabet $\Sigma$, and of the category MooreMch($\Sigma$) of Moore automata and Moore dynamorphisms over $\Sigma$ are presheaf topoi, and investigated their exponentials and subobject classifiers. Constructed free automata and free Moore automata over sets by respectively using the left adjoints of the forgetful functors from Dyn($\Sigma$) and MooreMch($\Sigma$) into the category of sets (which assign to each automaton or Moore automaton its set of states). Proved that each regular language over $\Sigma$ corresponds to the evaluation of the characteristic morphism associated with the inclusion of the empty subautomaton at the initial state of the accepting automaton.

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B.S. in Computer Science. Undergraduate Thesis
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Theorem Proving.
Developed an implementation of the well-known theorem prover of R. Boyer and J.S. Moore characterized by allowing the definition of inductive objects and recursive functions, and using induction on well-founded orders as an essential part of theorem proving itself.