The following predicate logic formulas is invalid: Vx, 3y.P(x,y) = 3y, Vx.P(x, y) Indicate which of the following are counter models for this formula and briefly explain your reasoning. 1. The predicate P(x,y) ::= y+x = 1 where the domain of discourse is N. 2. The predicate P(x,y) ::= y·x = 2 where the domain of discourse is R without 0. 3. The predicate P(x,y)::= yxy = x where the domain of discourse is the set of all binary strings, including the empty string 2.

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Inference in AI

The inference is finding a conclusion or result based on any data, events, and any information. Usually, there will be a set of conditions and the conclusion is made, which satisfies all the given conditions are true. The conclusion is made according to the inference rules. Any artificial intelligence agent or an intelligent system uses the inference engine to find a better result or output. The work of the inference engine is to analyze the fact and figures based on all circumstances. After the analysis, the machine concludes this fact and gives it to the agent. The agent uses this conclusion for further processing and decision-making. Intelligent systems will generate new logic from existing ones based on the facts.